好久没更新了，之前的补一篇

Oops! Ψ is not good for encrypt, but good for gift.

from sage.all import *
from Crypto.Util.number import *
from hashlib import md5

class RSA():
    def __init__(self, nbits):
        self.nbits = nbits
        self.p, self.q = self.getPrimes()
        self.n = self.p*self.q
        self.Gift = self.Gift()
        self.priv, self.pub = self.keyGen()
        
    
    def getPrimes(self):
        nbits = self.nbits
        p = random_prime(2^(nbits-1),lbound=2^(nbits-2))
        q = random_prime(2^(nbits-1),lbound=2^(nbits-2))
        while p == q:
            q = random_prime(2^(nbits-1),lbound=2^(nbits-2))
        return p,q
    
    def Gift(self):
        p,q = self.p, self.q
        return (p^2 + p + 1)*(q^2 + q + 1)
    
    def keyGen(self):
        nbits = self.nbits
        while True:
            d = randint(2^(nbits//4),2^(nbits//2))
            if gcd(d,self.Gift) != 1:
                d = randint(2^(nbits//4),2^(nbits//2))
            e = pow(d,-1,self.phi)
            return (self.p,self.q,self.n,e,d),(self.n,e)
    

RRR = RSA(512)

bp = long_to_bytes(int(RRR.p))
FLAG = 'SCTF{'+md5(bp).hexdigest()+'}'


print(f'N = {RRR.n}')
print(f'e = {RRR.pub[1]}')

'''
N = 32261421478213846055712670966502489204755328170115455046538351164751104619671102517649635534043658087736634695616391757439732095084483689790126957681118278054587893972547230081514687941476504846573346232349396528794022902849402462140720882761797608629678538971832857107919821058604542569600500431547986211951
e = 334450817132213889699916301332076676907807495738301743367532551341259554597455532787632746522806063413194057583998858669641413549469205803510032623432057274574904024415310727712701532706683404590321555542304471243731711502894688623443411522742837178384157350652336133957839779184278283984964616921311020965540513988059163842300284809747927188585982778365798558959611785248767075169464495691092816641600277394649073668575637386621433598176627864284154484501969887686377152288296838258930293614942020655916701799531971307171423974651394156780269830631029915305188230547099840604668445612429756706738202411074392821840
'''

题目描述猜测 gift 就是 phi

$ed= 1 +k(p^2+p+1)(q^2+q+1)$

令 s = p+q，最后得到表达式

$ed= 1 +k(n^2+ns+s+s^2-n+1)$

二元copper算出 s 和 k ，最后解方程得到 p

import hashlib
from Crypto.Util.number import *
import itertools

def small_roots(f, bounds, m=1, d=None):
    if not d:
        d = f.degree()

    R = f.base_ring()
    N = R.cardinality()

    f /= f.coefficients().pop(0)
    f = f.change_ring(ZZ)

    G = Sequence([], f.parent())
    for i in range(m + 1):
        base = N ^ (m - i) * f ^ i
        for shifts in itertools.product(range(d), repeat=f.nvariables()):
            g = base * prod(map(power, f.variables(), shifts))
            G.append(g)

    B, monomials = G.coefficient_matrix()
    monomials = vector(monomials)

    factors = [monomial(*bounds) for monomial in monomials]
    for i, factor in enumerate(factors):
        B.rescale_col(i, factor)

    B = B.dense_matrix().LLL()

    B = B.change_ring(QQ)
    for i, factor in enumerate(factors):
        B.rescale_col(i, 1 / factor)

    H = Sequence([], f.parent().change_ring(QQ))
    for h in filter(None, B * monomials):
        H.append(h)
        I = H.ideal()
        if I.dimension() == -1:
            H.pop()
        elif I.dimension() == 0:
            roots = []
            for root in I.variety(ring=ZZ):
                root = tuple(R(root[var]) for var in f.variables())
                roots.append(root)
            return roots
    return []

n = 32261421478213846055712670966502489204755328170115455046538351164751104619671102517649635534043658087736634695616391757439732095084483689790126957681118278054587893972547230081514687941476504846573346232349396528794022902849402462140720882761797608629678538971832857107919821058604542569600500431547986211951
e = 334450817132213889699916301332076676907807495738301743367532551341259554597455532787632746522806063413194057583998858669641413549469205803510032623432057274574904024415310727712701532706683404590321555542304471243731711502894688623443411522742837178384157350652336133957839779184278283984964616921311020965540513988059163842300284809747927188585982778365798558959611785248767075169464495691092816641600277394649073668575637386621433598176627864284154484501969887686377152288296838258930293614942020655916701799531971307171423974651394156780269830631029915305188230547099840604668445612429756706738202411074392821840

R.<s,k> = PolynomialRing(Zmod(e))
f = 1+k*(n^2+n*s+s+s^2-n+1)

bounds=(2^512,2^256)
print(small_roots(f , bounds , m=1 , d=4))
print(root)

bp = long_to_bytes(int(p))
flag = 'SCTF{'+hashlib.md5(bp).hexdigest()+'}'
print(flag)

不完全阻塞干扰

Our support forces had a hard time recovering some of the information, hard but useful.

# The ship crashed into the sun, causing a massive magnetic storm
#part of script
msg = bytes_to_long(FLAG)
n = p^5*q^2
phi = p^4*(p-1)*q*(q-1)
e = 65537
d = inverse(d,phi)
c = pow(m,e,n)
# c = 145554802564989933772666853449758467748433820771006616874558211691441588216921262672588167631397770260815821197485462873358280668164496459053150659240485200305314288108259163251006446515109018138298662011636423264380170119025895000021651886702521266669653335874489612060473962259596489445807308673497717101487224092493721535129391781431853820808463529747944795809850314965769365750993208968116864575686200409653590102945619744853690854644813177444995458528447525184291487005845375945194236352007426925987404637468097524735905540030962884807790630389799495153548300450435815577962308635103143187386444035094151992129110267595908492217520416633466787688326809639286703608138336958958449724993250735997663382433125872982238289419769011271925043792124263306262445811864346081207309546599603914842331643196984128658943528999381048833301951569809038023921101787071345517702911344900151843968213911899353962451480195808768038035044446206153179737023140055693141790385662942050774439391111437140968754546526191031278186881116757268998843581015398070043778631790328583529667194481319953424389090869226474999123124532354330671462280959215310810005231660418399403337476289138527331553267291013945347058144254374287422377547369897793812634181778309679601143245890494670013019155942690562552431527149178906855998534415120428884098317318129659099377634006938812654262148522236268027388683027513663867042278407716812565374141362015467076472409873946275500942547114202939578755575249750674734066843408758067001891408572444119999801055605577737379889503505649865554353749621313679734666376467890526136184241450593948838055612677564667946098308716892133196862716086041690426537245252116765796203427832657608512488619438752378624483485364908432609100523022628791451171084583484294929190998796485805496852608557456380717623462846198636093701726099310737244471075079541022111303662778829695340275795782631315412134758717966727565043332335558077486037869874106819581519353856396937832498623662166446395755447101393825864584024239951058366713573567250863658531585064635727070458886746791722270803893438211751165831616861912569513431821959562450032831904268205845224077709362068478

cert.pem

私钥证书的一部分，手动转换成16进制，

根据c的大小判断出p，q是1024bit 的，n是 7168 bit 的

根据他们的大小按顺序提取出n、e、d、p、q

30 82 08 15
02 82 03 80
06 7f 0a a4 e9 74 a6 3a 1f fe 8d 5c 23 e5 d3 c4 31 65 3a e4 1c c7 46 f3 05 f6 2a 9f 19 3f 22 48 6c b7 ef 1b 27 56 34 81 8f 46 d0 75 2a 51 39 e1 99 18 27 1f a0 d7 d2 7b c6 60 d2 b7 24 14 d0 8e a5 2c 88 37 f9 49 c7 ba ec c3 02 9b a3 17 27 ef 3b f1 20 d9 92 6c 02 d7 41 2f 18 7e 98 dc 56 dd 07 b9 87 d2 cc 19 1a d5 61 64 a1 44 f2 8b 2f 70 a1 5d 10 55 88 a4 f2 7f bb 28 91 fc 52 7b d6 89 0a 5f 79 5b 5c 48 47 6a 6b f9 df b6 7b 7e 1e bc 7b 1b 08 6c d2 8b 58 c6 89 55 bf df 44 ec ce 11 ff ac df 65 45 51 b1 59 b7 83 20 40 cc 28 ee 8e be a4 8f 86 72 d5 3e 3d e8 8f cf bb 5f b2 76 b5 03 88 0d d3 4d 59 93 33 5d df 8c cb 96 c1 b4 d7 9f 50 2d 72 10 47 65 ad 9c 2b 18 58 a1 7a f3 d5 be 44 fa 3c bf 4b 8e eb 94 2a a3 94 2a 38 71 d2 c6 5a c7 02 89 12 3f c2 e9 f9 b2 5c bf cb d7 84 10 96 06 0f a5 04 c3 a0 7b 59 14 93 c6 4c 88 d0 bb 45 28 5a 85 b5 f7 d5 9d b9 8f aa 00 c2 cd 3f bb 63 da 59 92 05 f1 ca b0 df 52 cf 7b 43 1a 0e e4 a7 e3 56 96 54 6c e9 d0 3e f5 95 ec ee 92 d2 14 2c 92 e9 7d 27 44 93 97 03 45 5b 4c 70 de c2 7c 32 1e c6 b8 3c 02 96 22 e8 3a 9e 0d 55 d0 b2 58 d9 5d 4e 61 29 18 65 dd a7 6d c6 19 fc e9 57 79 90 42 9c 6e 77 e9 d4 07 81 e3 b2 f4 49 70 1b 83 e8 b0 c6 c6 6e b3 80 f9 64 73 e5 d4 22 ef ee 8b 2b 0e 88 b7 16 b0 0a 79 c9 d5 14 ca 3a d9 d2 de e5 26 60 9f f9 54 17 32 a4 19 8d 11 b9 db fb b2 e5 5c 24 d8 0e a5 22 d0 78 6e 33 55 f2 36 06 a5 d3 8a 72 de 4e ef c8 b6 bf c4 82 24 8a 28 62 cb 69 d8 e0 e3 d3 16 59 7d a9 d8 08 28 be 85 05 4f af 15 fc 36 9c aa ca fb 81 5c 69 73 c1 71 94 06 83 d5 6a 1a 19 67 b0 9b 7f fa 3f be 5b 2e 08 69 97 59 d8 4d 71 60 3f 51 64 47 69 6b b2 73 22 a6 9f 39 f6 ca 25 3e 00 dc 95 55 d5 f9 73 28 07 0c 46 7f 36 63 cc 48 9a ad 13 0f 28 c4 2f 35 bf 88 c5 71 92 0a b9 2a cb 8f 75 d0 3e 35 a7 51 03 c5 bd 96 f0 61 c9 6b d0 2a f6 e1 d1 91 b0 dd 16 4b c7 21 37 70 03 ed bf 5d 3e f6 5a 5e 90 46 38 53 56 b5 21 62 3b ee 37 f1 64 85 0a 0a 7a fb 0e d4 e7 e8 bd 9a fe 12 98 f7 d5 32 bc 9a d9 41 81 2d 33 2a ec e7 5d 1c cc b1 ff 69 fd 42 b3 1f 24 8a e5 79 d9 e0 d6 a1 4b 05 46 e7 84 ba 94 0e 32 bd 01 c3 95 df 8f f4 58 40 40 46 2b 54 79 fa 07 33 6d 50 3d c3 32 e7 0f c0 6d 94 63 29 7f c0 42 b6 23 d5 6f 87 ef aa 52 5a 9b 58 0e 31 4d 90 d1 21 18 93 ed 40 7a 26 50 8d ea a0 a1 3c 9e e8 c9 02 b9 e1 c3 a0 2f e9 a5 14 52 c0 2e e7 bd cc 85 c0 ef f6 38 91 e2 47 03 bd 26 5d 9c 9d bf 45 6e 2a f9 40 95 38 bc e0 fe cc 7e ba b2 02 66 aa ab 06 c7 66 c3 ea 6c da 9c b9 ba 5e 1d 02 4b 7d c3 d7 3e 76 f6 a3 33 19 7b ad 87 c4 fb 34 d5 65 a0 01 4a ac 72 82 5e 41 ad cf ea da dc 87 ac ef 40 ad 84 b7 c5 56 91 ab ad 56 1b e0 55 0e a0 a9 88 47 0c 42 74 32 ac b8 fe b2 b9 d2 d2 59 8f b2 08 9b b9 1b bd 9c b1 99 e8 92 d3 61 64 d8 bf 3e cd 54 57 6a 97 13 40 47 a1 2d a8 42 07 48 5b b4 e5
02 03
01 00 01
02 82 03
80 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
02 81 81
00 80 63 d0 a2 18 76 e5 ce 1e 21 01 c2 00 15 52 90 66 ed 99 76 88 2d 10 02 a2 9e fe 0f 2f df cc 27 43 fc 9a 4b 5b 65 1c c9 71 08 69 9e ca 2f b1 f3 d9 31 75 ba e3 43 e7 c9 2e 4a 41 c7 2d 05 e5 70 19 40 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
02 81 81
00 e4 f0 fe 49 f9 ae 14 92 c0 97 a0 a9 88 fa 71 87 66 25 fe 4f ce 05 b0 20 4f 1f df 43 ec 64 b4 da c6 99 d2 8e 16 6e fd fc 75 62 d1 9e 58 c3 49 3d 91 00 36 5c f2 84 0b 46 c0 f6 ee 8d 96 48 07 17 0f f2 c1 3c 4e b8 01 2e ca b3 78 62 a3 90 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

可以看出是p和q的高位泄露攻击，也用二元copper解

exp:

import itertools
from Crypto.Util.number import *

def small_roots(f, bounds, m=1, d=None):
    if not d:
        d = f.degree()
    R = f.base_ring()
    N = R.cardinality()
    f /= f.coefficients().pop(0)
    f = f.change_ring(ZZ)
    G = Sequence([], f.parent())
    for i in range(m + 1):
        base = N ^ (m - i) * f ^ i
        for shifts in itertools.product(range(d), repeat=f.nvariables()):
            g = base * prod(map(power, f.variables(), shifts))
            G.append(g)
    B, monomials = G.coefficient_matrix()
    monomials = vector(monomials)
    factors = [monomial(*bounds) for monomial in monomials]
    for i, factor in enumerate(factors):
        B.rescale_col(i, factor)
    B = B.dense_matrix().LLL()
    B = B.change_ring(QQ)
    for i, factor in enumerate(factors):
        B.rescale_col(i, 1 / factor)
    H = Sequence([], f.parent().change_ring(QQ))
    for h in filter(None, B * monomials):
        H.append(h)
        I = H.ideal()
        if I.dimension() == -1:
            H.pop()
        elif I.dimension() == 0:
            roots = []
            for root in I.variety(ring=ZZ):
                root = tuple(R(root[var]) for var in f.variables())
                roots.append(root)
            return roots
    return []

n = 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
c = 145554802564989933772666853449758467748433820771006616874558211691441588216921262672588167631397770260815821197485462873358280668164496459053150659240485200305314288108259163251006446515109018138298662011636423264380170119025895000021651886702521266669653335874489612060473962259596489445807308673497717101487224092493721535129391781431853820808463529747944795809850314965769365750993208968116864575686200409653590102945619744853690854644813177444995458528447525184291487005845375945194236352007426925987404637468097524735905540030962884807790630389799495153548300450435815577962308635103143187386444035094151992129110267595908492217520416633466787688326809639286703608138336958958449724993250735997663382433125872982238289419769011271925043792124263306262445811864346081207309546599603914842331643196984128658943528999381048833301951569809038023921101787071345517702911344900151843968213911899353962451480195808768038035044446206153179737023140055693141790385662942050774439391111437140968754546526191031278186881116757268998843581015398070043778631790328583529667194481319953424389090869226474999123124532354330671462280959215310810005231660418399403337476289138527331553267291013945347058144254374287422377547369897793812634181778309679601143245890494670013019155942690562552431527149178906855998534415120428884098317318129659099377634006938812654262148522236268027388683027513663867042278407716812565374141362015467076472409873946275500942547114202939578755575249750674734066843408758067001891408572444119999801055605577737379889503505649865554353749621313679734666376467890526136184241450593948838055612677564667946098308716892133196862716086041690426537245252116765796203427832657608512488619438752378624483485364908432609100523022628791451171084583484294929190998796485805496852608557456380717623462846198636093701726099310737244471075079541022111303662778829695340275795782631315412134758717966727565043332335558077486037869874106819581519353856396937832498623662166446395755447101393825864584024239951058366713573567250863658531585064635727070458886746791722270803893438211751165831616861912569513431821959562450032831904268205845224077709362068478
e = 0x10001
p_h = 0x008063d0a21876e5ce1e2101c20015529066ed9976882d1002a29efe0f2fdfcc2743fc9a4b5b651cc97108699eca2fb1f3d93175bae343e7c92e4a41c72d05e57019400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
q_h = 0x00e4f0fe49f9ae1492c097a0a988fa71876625fe4fce05b0204f1fdf43ec64b4dac699d28e166efdfc7562d19e58c3493d9100365cf2840b46c0f6ee8d964807170ff2c13c4eb8012ecab37862a3900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

R.<x,y> = PolynomialRing(Zmod(n))
f = (p_h + x)^5 * (q_h + y)^2
res = small_roots(f,(2^496,2^400),m=2,d=3)
# print(res)
p = p_h + res[0][0]
q = q_h + res[0][1]

phi = p^4*(p-1)*q*(q-1)
d = inverse(e,phi)
m = pow(c,d,n)
print(long_to_bytes(m))

# SCTF{0ne_4rgum3nt_1s_r0tt3n_0r4ng3s,_th3_wh0le_cert1fic4t3_1s_r0tt3n_0r4ng3s:XD}

Whisper

Two public key certificates were monitored. And Mr. Dual intercepted a ciphertext. Just when he was in the rough, a Careless Whisper told that the length of a key parameter is carelessly set to 345 bits.

cipher.txt

1	CO麲鄌i棩T赁\|熠漾?t紎m\|L_??`[玩鉝o`{鍼81?T拵A囅瘭鲐Fq[麲暡.!n庆?m丁漝檋??ｅ?z螨丼O媍虱亻鳧蹌{ｋV

cert1.pem

cert2.pem

考点：Dual RSA

本质上是不同的模数共享同一个公钥和私钥指数

代码表示：

1 2	assert int(pow(pow(0xdeadbeef, e, n1), d)) == 0xdeadbeef assert int(pow(pow(0xdeadbeef, e, n2), d)) == 0xdeadbeef

同上题一样提取出n，e，发现 e是一样的，而且 d的大小在n 的0.337左右

exp：

[61dctf]rsa - S4tan - 博客园 (cnblogs.com)

from sage.all import *
import math
import itertools
import libnum

def matrix_overview(BB):
    for ii in range(BB.dimensions()[0]):
        a = f'{ii:02d} '
        for jj in range(BB.dimensions()[1]):
            a += ' ' if BB[ii, jj] == 0 else 'X'
            if BB.dimensions()[0] < 60:
                a += ' '
        print(a)

def dual_rsa_liqiang_et_al(e, n1, n2, delta, mm, tt):
    N = (n1 + n2) // 2
    A = ZZ(math.floor(N**0.5))

    _XX = ZZ(math.floor(N**delta))
    _YY = ZZ(math.floor(N**0.5))
    _ZZ = ZZ(math.floor(N**(delta - 1./4)))
    _UU = _XX * _YY + 1

    M = Matrix(ZZ, [[A, e], [0, n1]])
    B = M.LLL()
    l11, l12 = B[0]
    l21, l22 = B[1]
    l_11 = ZZ(l11 // A)
    l_21 = ZZ(l21 // A)

    modulo = e * l_21
    F = Zmod(modulo)

    PR = PolynomialRing(F, 'u, x, y, z')
    u, x, y, z = PR.gens()

    PK = PolynomialRing(ZZ, 'uk, xk, yk, zk')
    uk, xk, yk, zk = PK.gens()

    PQ = PK.quo(xk * yk + 1 - uk)
    f = PK(x * (n2 + y) - e * l_11 * z + 1)
    fbar = PQ(f).lift()

    gijk = {}
    for k in range(mm + 1):
        for i in range(mm - k + 1):
            for j in range(mm - k - i + 1):
                gijk[i, j, k] = PQ(xk**i * zk**j * PK(fbar)**k * modulo**(mm - k)).lift()

    hjkl = {}
    for j in range(1, tt + 1):
        for k in range(math.floor(mm / tt) * j, mm + 1):
            for l in range(k + 1):
                hjkl[j, k, l] = PQ(yk**j * zk**(k - l) * PK(fbar)**l * modulo**(mm - l)).lift()

    monomials = []
    for k in gijk.keys():
        monomials += gijk[k].monomials()
    for k in hjkl.keys():
        monomials += hjkl[k].monomials()

    monomials = sorted(set(monomials), reverse=True)
    assert len(monomials) == len(gijk) + len(hjkl)
    dim = len(monomials)

    M = Matrix(ZZ, dim)
    row = 0
    for k in gijk.keys():
        for i, monomial in enumerate(monomials):
            M[row, i] = gijk[k].monomial_coefficient(monomial) * monomial.subs(uk=_UU, xk=_XX, yk=_YY, zk=_ZZ)
        row += 1
    for k in hjkl.keys():
        for i, monomial in enumerate(monomials):
            M[row, i] = hjkl[k].monomial_coefficient(monomial) * monomial.subs(uk=_UU, xk=_XX, yk=_YY, zk=_ZZ)
        row += 1

    matrix_overview(M)
    print('=' * 128)

    B = M.LLL()

    matrix_overview(B)

    H = {i: 0 for i in range(dim)}
    for j in range(dim):
        for i in range(dim):
            H[i] += PK((monomials[j] * B[i, j]) / monomials[j].subs(uk=_UU, xk=_XX, yk=_YY, zk=_ZZ))
    H = list(H.values())

    PQ = PolynomialRing(QQ, 'uq, xq, yq, zq')
    uq, xq, yq, zq = PQ.gens()

    for i in range(dim):
        H[i] = PQ(H[i].subs(uk=xk * yk + 1))

    I = Ideal(*H[1:20])
    g = I.groebner_basis('giac')[::-1]
    mon = [t.monomials() for t in g]

    PX = PolynomialRing(ZZ, 'xs')
    xs = PX.gen()

    x_pol = y_pol = z_pol = None

    for i in range(len(g)):
        if mon[i] == [xq, 1]:
            print(g[i] / g[i].lc())
            x_pol = g[i] / g[i].lc()
        elif mon[i] == [yq, 1]:
            print(g[i] / g[i].lc())
            y_pol = g[i] / g[i].lc()
        elif mon[i] == [zq, 1]:
            print(g[i] / g[i].lc())
            z_pol = g[i] / g[i].lc()

    if x_pol is None or y_pol is None or z_pol is None:
        print('[-] Failed: we cannot get a solution...')
        return

    x0 = x_pol.subs(xq=xs).roots()[0][0]
    y0 = y_pol.subs(yq=xs).roots()[0][0]
    z0 = z_pol.subs(zq=xs).roots()[0][0]

    assert f(x0 * y0 + 1, x0, y0, z0) % modulo == 0

    a0 = z0
    a1 = (x0 * (n2 + y0) + 1 - e * l_11 * z0) // (e * l_21)

    d = a0 * l_11 + a1 * l_21
    return d

if __name__ == '__main__':
    delta = 0.334
    mm = 4
    tt = 2

    n1 = 0x1b5d4fe0aa6782e275d4ce12a6d57562efbbe7db6f5277255b891729bfa2a18d3edb49843d7989a37b9516be2df8ca939058e65f64b5fb2071bea4f5f8d1392895b32bf0377d99f4f79979125e5db01cdb5080a1c2d665c9ac31b5823025499c9513277bae5e7a846cd271c4396e2ba219020e58a9055cb18a28d36a00bf717b
    e = 0x079f5ccc665767b4a257e5c1ff56e9803df2e5650302daad420105fe672447743bd3f0bea1c46a4987932e9a886ca87a7afd7796abf1e5629c4986fe4f22e89cdce7abb06624465146a2e2b6ca9ab3196ceab7467974c1dc45608a200411b291fdaf99f7d80dce4db3566f4a9e2e574c6224cd07d80638d28f7820bcf4b49143
    n2 = 0x071c324e8769493187c15f72d5cc695729b48488ee3fbd01db00d5c478f08c7cf32093ba61745051d3e9d169523aa91438181f47679aff5edd22950f74a1eb1443320aaa5d97f5c1e81b5ef9a3e69ba669abc4c6c4b405f5088a603a74f9bcef88823b4523574114c810600838728196f8e5e0d4aeeeeab79dd8683a72f3c017

    d = dual_rsa_liqiang_et_al(e, n1, n2, delta, mm, tt)
    print(d)

    with open('ciphertext.txt','rb') as f:
        c = (libnum.s2n(f.read()))
    m = pow(c,d,n1)
    print(libnum.n2s(m))

# b'SCTF{Ju5t_3njoy_th3_Du4l_4nd_Copper5m1th_m3thod_w1th_Ur_0wn_1mplem3nt4t10n}'

LinearARTs

Young people should have martial arts ethics. I see u are exceptionally gifted and has an astonishing constitution.

chall.sage

from random import choices
import json
from sage.all import *
from Crypto.Util.number import *
from sage.groups.perm_gps.permgroup_named import SymmetricGroup



def Young(FLAG):
    f = int.from_bytes(FLAG, "big")
    q = 65537

    s = []
    while f:
        s.append(f % q)
        f //= q
    s = vector(GF(q), s)

    n, m = len(s), len(s) ** 2

    A = Matrix(GF(q), m, n, lambda i, j: randint(0, q - 1))
    e = vector(choices(range(2^8), k=m), GF(q))*Matrix(ZZ,PermutationGroupElement(SymmetricGroup(m).random_element()).matrix())
    b = (A*s) + e


    return A,b


def Old(m, nbits):
    Sn = SymmetricGroup(m)
    p = [getPrime(360) for i in range(m)]
    N = sorted([getRandomNBitInteger(nbits) for _ in range(m)])
    S = []
    for i in range(m):
        r = [N[_] % p[i] for _ in range(m)]
        r = vector(ZZ,r)

        Per = Sn.random_element()
        P = PermutationGroupElement(Per)
        Pm = Matrix(ZZ,P.matrix())
        r *= Pm
        S.append(r)
    S = matrix(ZZ,S)

    with open('Old.matrix','w') as f:
        json.dump({"S": str(list(S)),"p": str(p)}, f)
    
    return N

def chall(nn):
    # The challenge lasted nn rounds
    # Young_level * virtue >= Old_level , where virtue = nn + 1

    h = []
    HP = []
    MP = []
    Old_level = 625*2*2
    Young_level = 25*5*5*2

    M = getPrime(Old_level)
    XP = getRandomRange(1,M)
    for _ in range(nn):
        a = getRandomRange(1,M)
        b = a*XP % M
        HP.append(a)
        MP.append(b)
        delta_level = Old_level - Young_level
        h.append(b >> delta_level << delta_level)


        

    return XP,M,HP,MP,h
    

mm = 16
nn = 9
nbits = 3840


A,b = Young(FLAG)
N = Old(mm, nbits)

XP,M,HP,MP,h = chall(nn)

# MP is useful ,I can use him to cast five lightning spells
D = diagonal_matrix(GF(0x10001),N+MP)
Sn = SymmetricGroup(5*5)
Per = Sn.random_element()

P = PermutationGroupElement(Per)
PM = Matrix(GF(0x10001),P.matrix())




AA = A*D*PM

with open('D.matrix','w') as f:
    json.dump({"D": str(list(D))}, f)



# OK! Find your martial arts, and then you can get the flag.


with open("output.txt", "w") as f:
    json.dump({"AA": str(list(AA)), "b": str(b)}, f)


print(f'My SymmetricGroup is {Sn}, and my element is {Per}')
print(f'M = {M}')
print(f'h = {h}')
print(f'HP = {HP}')



'''
My SymmetricGroup is Symmetric group of order 25! as a permutation group, and my element is (1,23,2,13,3,16,15,6,22,18,14,4,25,11,20,24,21,9,5,17,7,19,10,12,8)
M = 309169501373330124045649100152326414225457160505584328527283516968464416389302355829097052128714780092162406614467026044744098784954762500832278190406881802198303575338158311874491341970444579146638248815636164413771772581964591833455055886833879504320098506335328910379223983277573694356846337961823081287986674791459748001014087760336006966850192999063236788568848765812192775492248445517060690151700498331622538367493718859724934115228375142396923937735633684527869745420378950550480692200706066019831688796077313463059296313396035429537407627377675974680696279162072713257960965681304091009329215383850223530139165455326927677102783057396241883175412729216204807235187239596365892879371542214145426492827777125727970815789114727245511828912252143569
h = [3565625090222584896920916237461241765625829204082396377386021101162536812411479309464325956424849651112502540095796665989782448302150047491000013081443589381171861802823657878857754676608742927932812781165716659755896099505195018830422885342733139127785165794897376463794696074605473512720672450888626374504772116915620258088753289255996096552892614801083370595759624402874902282635442418547645823133641783382626721416313803991932439793168113855890150599332984583295219543856049901518912201443065300476561372304830840276820139993555523469165273121628823953454126151208689489078628524850757272649061955436843893289237414654732290904213005377463766762255194199607599718375650615493280298611532927519686558670313416090562438894368509350896602591065538560, 286740894693471986151090603562932147965458822098297907353215124508138484491994267754471216888566417392843923796488725160656461314962959042706124173470952968241147487040483767911639159119505992553207913863135028688626896196178757909088128827455625174341894140582939848620368540355056452428553556546413465430152617836247505772663758606552662729528340901377490256234099815707208769579251833692482247933846648593307680305448986314447242583396656418769737861680456297522358131674037354880608888487272985141452871763297604747444764332049229204365395410106847606241968638474099061876569990163879954288002836750959104349076854993248516655758322107956062243468530601256243967323153547535726777712582210098524981336526310800007425464476736381605758610129914167296, 202445786178968197828946112166667682571891905248793492278433983415264905988886412319222803698650008275405441752508434114212113517053913972304515710532012288036732448805044856628337036478357496484044773293960097063848568051250774170422935810965491124102107450786197166927290614807575403261921855599437944525251033428950982061449203659272914014109623656149839199935645660386382459896840619916225080206084500617856222897968865436783548821187873430635315967325778835200418210099836625362334832448337496843986398001079590846483593452928602841826412074751479179471599709999916393508418744578599831517548843854866251289525136765297969136698285441109232446206843977149859059568434871554288377088102779550812057943402777376610057499017696210394059743209313009664, 114630215368349491250326648494149748728124718005857201833657753308980378360823813480094685056650954220208569495921715772409260048257134505583210349697604470912610748671738387322753221966031149012764535612682778184882174392537951540598166408100353995693537007226929298573802177602978136134506604598926968767277963229517115896872176785224081721198822306288029114228955110090342800494317915814873698062519566559427796027618459996738296291782097320521350172532923653864250838232011730592925952612867718426259229217480911558421879422300001641170190840092379605603655701803649801243406059797147753118709730213303123683329677068533772082060407549189564758770771711148071596602056935716438347268248190581386987972757911856155781563899140822797888004226036006912, 128249367678574240079270694387429301574447189368221420750047602082333294620192478593526403955673394674124614483528399397766799072294205407818283464218350759458734269850052374022374583516046462573242829813776315162366850512131805663098817008453376098230770350796562755291771240680188153978483320771657621585572523650775437065002970862224206343896650474078023744187172724827284900132434561870157274624749481073656218832950661419154809116630241897087363941068977482336058825222409922455565132842885044852488100437379745993397785019888492704177085025661715401393223084613786993440233186999961708361656323625565518221228007812487647507152403406194060777071074419667727156839380340460479471882700515901974677682591933244024896502221255164137619867236474814464, 59331241745881917257932833661253483407124868132789104057434303748460794035055450167305496229505776497962206681068504038089886777631651664100577079680933516972657892279730519042800959265778075851643260975944157575808540832473360789304763830393990596483325556391563383526131388426655998362610795663009444329530380313582369506744601127066018505286584082074112032220681653032998814836135211241601616761559477125123260865574463289315537641250468595444847485104869371846138937594815717839233479424297762637589843061706537365341325349697086472650360732699495909942722893269089976271337217878676728476285757191230122449283410993290558727101211299826258005529280347023431637543174327095221833097882251371141896661614980087581376418853642047359092191718247759872, 194175487858295065586566223420720835354218714701012787036868166885106803179611016852320235121944886794854103233580220709024806072743993477154116046455972680314714490810103482613775169723949822599089353607462687446238694112422779778557153306320141326888706724709408146840971915646939721136724368012432988045478440516756541030644897102338343015620307071124895653986756365725579987250601332133147888516462970772662004254372283824275049130754409522022155104472953510056515893487814795314057133448327072939691256835996305152489881345263632544581620669637374642183724635278556621665654137071320546871015687481523597402928763713183489458838102245889150936728919959706046092027960728825776566021949524779914956226078468441681639597976295123311554992063660425216, 115807966653135071136266364151575193370063353963428994232152558690537462513652457844803096649471511022423130391640990718769139833768597282872892832632006932256100725142377601958457582836326282142674470340977659300588249614977457789078637672424804434580082554677223019302922992562279282682989740074843377451539592513262883913515900320935326048141177654658002842824967867990878423576079246988742657580816398545604320575322509216636723893917401586976250940528255869144608693606581992658961868351662299980182039083401570931369157275822911645710245831972301615048181855392924402552747776587682847866506513589721569586179062186510923857682304736484524409943982860419833114775174973677241133994963586243092033231181717755422868113246798964708435895447826989056, 35892864763676162390876495832131732661057713103645821857653105944898881372368808709419507620431545862639883539544774550258981962490994311035563824804791343118179784911204081384298523734092852978345353083620780025983844560713535542579917199852557029443606552741189260726705956142592472777625642697686483587065598383553745177190736612246797880186504227507540789056735743669295160656843457591270441961646851151123270490417727787782300206183313402455683157806373799412772262389178947152383087432869175216907112201344491993073522598897459497720231382736974467891671184580545749653915968971302794570679028312275641136161418552643700105215949462752782765599606395043723535992514850129235084780569665298381129831228968986167487292913320768400938041503014453248]
HP = [182123398439336131233484419016500805950625530876289136147992418330368556518782504528500478328506268530182121028338611308706301778495117293952384271741141930454826813234222655694969514594179399691491676343267560926415204796892285953757083137635724586246679285504584200603423040990857955982592545447321735123888380669252758270022750955484747603018957220340523162322224297824154306196315662236519394066376582303992842999145368668536271548561974662730580382535581064544751603313110317522142473855128127879421866476758202400277448627166191464212616826131845112048518089279156877724351779259697512559047606602356481432326384500230304234630224805224043299183292854524931957718694768306272627669496947333830650701612740067754226344379590044087735385490127725862, 143170049879066655087340950742576943114220056125957541251904657597420632960015895981469092773424062349481612793313849969949143634455140221504418524950906026552571808412365313452770620316647140315635576351924131570731151371864300979486246561311374091503771233474221846682477948158595874825046725186096019808916856990568087679235183223125111635340379631262792582193894921427748477534899648278496684573736979116799130367368459501772350225298850161734598992871658808303947946703790369232633550983464071710073626283163523659905448412753809088559015473221667463885047754120012784534383142422681768521744011385759111784771218858429141270195947803513052066866898605116497618560152428747336114471742600059289342252682494024257280492765302681978041917175224445454, 181932081065216017223259767432026159751069100962417675256904857171174594214631105569878401257202843288868067795959660425655397502682572819329811836847256980387967545675607257191386494389870983892416162767006265255985611267066664459013834260578459679814704254643652527448346657946799415019242620362556994094217501805852227552561431064112972359577708305419407712233651342990435225577864469921706228376386943352990854043536613387681781610381704457332320684886669558444649325853462867815167473502469305672972117003639658784729134706896312010708005781941993559519054971159338636279746679220293668476785752715272037394473281514117697060980377364913173031572794672785720241295564153405600993322639561228795731008971285970805298272968367327982292736365952177736, 152197501838094386559667505260111556746524794647762036036984156853293482749405051706379215782024625767996604204199239858042655575156447769644733342469940464962491758196879181740442958683860120188153222622045687386550968060691333980045707578681522952010130720785366069103645756481641865768541014660604224000448808608848607142992914438243019336580286597455942208546183871629991237012627078724041815698483916930337697145596477943636313719062754662224057190310995369364817444976298713991954316505112491477110025799278176478205958831032614361098570277711286905522504386261323350696026797810604096448605140635754896533192146402989175530945145957561334345659035675075518654525640506611082619111666729303712983450765181951782352125875791130477959487243678637091, 13260127114160132039578764564277724908293717164091148143281881592450508800268944502885346275659282139962084615098549527321116911955505649119891798866789702019684393024690093331965422247341532921411724247274538089836518071897735012248880718279028139698315282234778842097294789834605571276706239190589177804771135138639650083317735678737873354475068162084129555751126946723880482765306519620594499615623179141020788167278111494656031619604249830332631535459164808166638124806843052957919064456863967475953053614347964520430672883482509352453640521720313380086324061829310129198351733197836811498655541708077300463414261809122652381872563486116022996781876662952751320598808796685963865092538114154484684417346701057121540968905340884852819266786655758589, 7726965701613058376939617426173930484905424609871511448979899585789330472291184137208473525618669017229437131718602138062693323242254540169837667647945751730728109543890184121875756549720616016417689684297714982752898170211522441794931085191911567142756874944612942983995000585648922927662513704308624388978740497618316239028274910398075357992565743563209649419566296437582035744561981287334953927069851636537379718348745797306743042426246174030053256711319421877929342022143063981126785133505358707977994735220823800241921524140116409926290245600210702333580796340264633188699655847265231481741281891892263047439742010063674785264961945504178892794083333407945969304699309469264200568906760592035714702098416830232068808480043043046899584880476365211, 180019050945153380400290419089497765220330628588910896281952550416089875088850281952204916892735263785902815673400396668990373595469072648699918494008065197996354855591310768398651316061183602708507734278231600299784123286043254063248471261126675877896352754705297219631260970186401862696837291306580096200621090959901083133979809165850290006958174043988594120292941019793669119321273860506863788556691180109910206811333775009617945993184652622929206661236756401337666271307645630166144277622050610823301758570383783302397752531144991093835433241988398747399949918853848203882961092951831645541246295873588649289531107814613167236073250185453276804880016561013769084225682634383784489652871867815664211238325551136693769474979447466046146633345857611195, 153629149463789849413429112784055293255734339122176408662359601604336509143473758509975758863274395783633189549584941125392600362702091233425733911049553699926215208790821097092121122480643207790283486114884596194662369389215802952635756543090033023067139610689568413680910122744788001731552268160061684744631583107942765508030881967516350806276166348479082293252825499156766363138008724860360262292088895234376252334258828427316419408016153682496909981178280572676774045522450227853270448821337580837554794712541359286413423248459963738684095208415746808201768526760043282181933350859027227907243501251390338333188167931974689538439823388790515993422873395205982049903304374197483641428361419371833919139638015039992779119950859870347438758668679332495, 276427336329209668688130277925589460360311327851014652110707325284581770430564994121969230515633704248812997375123175470056237355182594647858048847262042361717893313893682161435196235153101006253340527909451448103893104917041136181377802230394106849393237486928849495116195885563734324888330607632821513438897200091110205098807840437587357564885934968344589488833398453563587665373858111713149172110412979734635024012258145628247175689960363707897865274630069427102722542299814253018238192096822853168130596686909789751383470674093768125446566821380042192204089190375373896356618809538058749144194802493153530124585829617231928160073305696376878930156414497547968857648212679322981790227182840452493558367673102471438871220031633314842129410346869161197]
'''

D.matrix

{"D": "[(41793, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 60167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 4171, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 47491, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 51848, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 61108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 3645, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 27453, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 31091, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 52391, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59401, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 567, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26744, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29133, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8374, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58306, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30198, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10258, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39097, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 62336, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48264, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6386, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16791, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 34934, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19762)]"}

Old.matrix

{"S": "[(108032701991161449851369002312715580973354179025631833045125920330341444336132442627369167910196499846245375, 536708156806056194339800940453431360309948744802961091477684592805557756940577780671965778135111037727024460, 1092908539163523128210211825513206434685729471033351288310817570413536030332936913121881436496682004163218561, 319681218899114691143952029933390929281094479463796376994923082695907785812861868813064052001648547956430773, 1491469717762965437203234107675304739260134332073261473787166051408478205091597260393509384628194825690384017, 1373831114788217760848815706926510177900812033455370113335228787592380681943495789200016044894484593753473793, 721749134747261598156945357302901463050568624661297095403296472280731478071009708971832640575096673851818368, 1860163764050401633727513573627217696972941984286848985572281249857942774623702194570023403287105671073489060, 154984136256332584966107344852839904503587225305261779832283480159849061688311452179481908517673432437277241, 1561939838062660892618339034341951346106257548745672265144871883988280932734601893314037783804475701266891293, 1196621210864420273010964492926788183563258771458649486943239707342155163532184200078478415282614629395227800, 418140199208035988378436961769638766691045254816780694434194995467625611261074562013654661647238861824195187, 1566865563381296633840183260419394895718650714211270127110339192873464656390177925048966057251100807853472205, 591765854512223923173381833993118081655482569860165937279009553758243886824330666933325098097909951941773363, 1621194715625482277240801603470708569317091835690367023874070253760241984371512903868391207817859394152312002, 1853919209784660031160850930352771886269300975251430020793116172679096829612113956371814479169815876124349500), (429873231732555141667240718587687999822857219084121172009626130310358943388885080601718909981680593606929592, 696661257924439276997527001346014167032958774864009281004980339623413640279240542438501016146643735870840200, 705077116321796552136313163950148514272481595449062490800965253320667803690854999857493736016740764844951855, 36759636718531135702894811812498288161339459911344005228982773190594494346457316668225373274587742986714394, 199617109272238821758248859791496856102696174698246601793036123989271809739396262465329953679772767556175349, 748305044943665754868843090133175750486758697161694063451745527234017037314999816420606532108167584070014650, 128713556531371763123849284738409764132111189857502611935232398816796618991882300550609541403882964822025197, 720294314730287284918332403206366390340674935575928437196947060809525523697555946855032892796717502508756244, 772169734387893586465583421665818938650077225148817036618409173104456878749345815499342643475174237365342088, 485704538257264318281616202446430879022758621467258744613654741872135241670088891039125785177734123506788864, 1049386623703990774779796004447122771056640068769982963039740391255206084894449612397763605343929886627187755, 1353791534940584582018886955223018991871124918503240637355081780112975543362795028582394093562125315687397117, 96922325977204245215966615509244830479352553017235612165102140203380652402877156933626056845508236232145474, 1491547721205063194329451603221117324835280653935458186449353861087354977686600897202090908965745312062496462, 657985609407219294871212287937819792392394243075603163798767913815753294714053803551989285171175046026021292, 1321750505787806228413096336073233274921046205768894526421731637298008087552230154604733661782305913950019758), (1086778637488893363555155897651776469669479648114718713027748026839195873829973285681739101838980868002956926, 1603798106276423628680411507040686545422004273861779510586832810301991479137460804045160999460099332509348272, 1032596573594908905682883741312054579360541498136380107452641965336593376163298589305748612869488444382282785, 1722871599310215842537874903061856170822910917071612533538758545930106429737859314184812107888570570514436817, 888612741358369537511403754406447724251960233741122239049680647261856619404416530595695189652109281384865551, 272210091239236373983366324215208566923182631266812430374542000868950822203456368709019668399773194130115582, 998340433312163849536880381773142598561110062084017535938298827399228054526060914037893418142610051549344149, 416561209542736085163087421985348135859148177916787887874024056410059456662972557534961467733006653686852270, 12588651533966392617982800355146650879738320880541134139166541021872185894667746916875855764202920352998332, 239155589045658762407997613376641052079067501577649334701928033885172818297939378539262342760726229932149102, 1712700772384296868424330714519998133456916631419429384710641521922451158914619767158484746435503528247198201, 973460793536380374905536216000279457254227413270258748292701993424187048976790644495166672795707977339193401, 298374738199736157379773918814268251577739944514215745671393904924422066180617518790938312830200625034492336, 1084149657600176924628380982516941510886461179594063721146617624251927480674370653365654346812040758416587254, 1455486290142480470333195218741425003901972373269012398794854208385742131684661811551770676387271330305840033, 1317616016751494143133911076475028074618881097289669566979706802061473591757960790365356311174253283568545171), (511902046345644666272587656834397557926585465865594799110299385517243337669760460710245197553437169107076465, 1308330383856237915365466642984283736169698388215802844201751246880103558237647553782829473002257961428836670, 1155713813790080552487939803696106101790310975411071299829183870773444388451785801500623912616242544692680962, 1224908750816908679021939739243701563153232819921843770261166611815141376759933697069591681336679313105729046, 452063111929995491255412240376860357091791634348346543674689097860541694702190428064670811147941474189515940, 243905199413971842010848437083883170120387967869945489727874891785274619523120687843469628111008333520281173, 218012047981557163160906385736965875971834228229268545141409957804110200175228120318440102572613964108852241, 72449390352553126882641989616711201258083728722073811669248333042484356858555217373026830154484599675673166, 1744077638109996915648335389542463821997796324708102976212623303084662144503419047177392858024029202496884056, 1562406863302128494306184675628052746736729226148455257287537831013528914148133192444813931611184513898761964, 1370809565011874548553736664131319308120113144756404775592948258246558844114463308790143707574202284352297700, 619582693502976159201142244983464537147959560539005191107859790886253434688472547727851180959778494649468347, 1439935211405443869676158269127460181688799184642555475680575584652080501734744148715596139324976221138373651, 90545837187619363498470568359275825840618056784074308739892174914423452949587594590059370188451502082946781, 482428410735918416738432316622337711063850733413329084474254412765173029163913604186737203649136909991911512, 565434332235923074300308595897761005070298372508007151970717410598099167866385478749744466175454834261310565), (104491799965715411013561142125662618371589863368220043903880063313450364721340353778253423882215372628063760, 995180834506623008467226233521869342403315180509957213686517153423463062453889353398616389051090749137685843, 829565021944997397018498002084161459259275942202921212249684154592702614408845709428138511390580330061002946, 534327621921588874889149990448038480344105599605667358128347364437354685222101199440058722509498308377029012, 1132330464934751558500840836525167035985136508412935213102713347379055094835345081148822225633094652420795588, 450074048099726665802238274851908045566712843397793274051290281351600335456664818882443154184755479919306880, 799650301333724197381856809928105802660976183437036834013098030038374988250871838187978763436682367937424064, 186144160986287531641216966101956370994842371362686292130413967390643062283174363969086648192162770707299860, 908534860213206841686157605935550514698866576053159893786895113561156202467655121726907189182979000098180930, 45172777025563801245002587177051647086647015775396329903238685443215301743159050121404543533110450927794409, 764812910167477106544110492707407657402757978897081341870134647618267941562053074583099500973988509251503866, 725981463002339136952211983895345042866512126776025275961573441253428056712570870615698244996644709842695281, 835069084199672363874718204938215438544707590888115425961659825606911679990035477671978178973889650313585055, 1191875778351256270634615082284082976487567969444268263184598475937048145998543269062890189570330392643703428, 83818590739829464348451185348616535829221962242907104691853650713849624215858867979607119022934848835272741, 845663971836096838373625947207777962185246822459741259152503695147222855185127535612579592810063372388393425), (730080740708716696869611500305945729582831639692674576181815669256588053495445644654846273425696381106798213, 1211401865625606862892141164094862255157602687290011401877324564094913451780788011572602838694851127273686199, 761750678069382705088989341593202296445602247339072406661067951708499074600129843633749860027539961169263821, 958488935282214627573417363369674085278816875474745585966084121728154471973830854061042022718110987983758533, 1000154070884484290117374350945928521584252400077614217868317402688302271277639661314255973413082836976423525, 452737780943126759615159828372843517970855322695027226969144987933644903011529013014573924533431359051256850, 5805599200676249107157522629732437488517848218120336534559572461215244230092132165434652875158210784360605, 1069648823350032633271251526144211153517485574227702676510205431642788090278206667447057508392521720178991564, 464345016404000464145764099641622835761022772300106935701609296071422986154529936480523330102784677377267972, 887532013540448997976095141800168404616145524208067918411064213199200246544405630618505727647904031437367765, 764896944683051632934376964111352690545726493595561980325842532869416551338993800555386022016655600198592863, 834595492951168051763345064768685082923666710575447603461271875560636579185091403924607285606904089495798238, 97747066740378772563805036049036560981941178276358675793741851520890271416061851970734762331332677029558286, 1291639614271453651479090561671509420789047119165785858217334853499388375967049382736266913449874753320474210, 801271538360332225899343978692624588068282915247341176248413743892071353524747855777605347936971072256796883, 583118453726128867307239318601314573717226612564585476755251111771273736693625440352334611064633212563236599), (1007558687762692623401107502108785671552540294554027553075253821535448496219183688214829259558409405603001724, 82954089525210775107785196754975536343868930175076975506233700714273434584908468192257652423060749000141288, 427447460947692981480247356494758073766902779792449397588581408107838459193575936867213556781504157624146419, 1374117754996529221098536377009433889631952516241548318835190450059797631046672640835049895872866758924481496, 156038208432623159135025608204515658053054306527311311313875093413737186414935362808963926062607056191492625, 1515640320653109406794405070206667431846552825063179966889387609909437205938636205039178430345232101643703029, 1001238386683833647397450794067318370920199592087688426532041695022589977781759577351271154279661457711401139, 9286812100870995351874739983837536749531703373251036760857092007083527341690165710076770799982026349469295, 781398522411624239036136435439321625771428352649403511374119891867804110627699867915291152830172439999673301, 288390340485689855297713282913031890061650435198757756679240034152731783902546010542111152853837802947107198, 1282499438978850273310621141487984553225042108684339648738689012516484353852213933474138478066589426905792640, 1206882588472439544838766692591222446845991327532088581599851103973276440986865610584267969223571059209838017, 716745202356877068654799969764658910268422168331996123562556456205494558399089053935448159249370428497961068, 986593095310489014203641425333005980037776378229232672361107883934927730326718162983564623505526232068548290, 103772617718005675720056677269973171337468439536802857689497610845701001446000293596756576084101670871872394, 579163101347014044284264738999794759737770512095227857962630915400460939984272909004056647376161945305737747), (288435034175969956020092056225392604045743897118720404871671986231084818165458292729640648522613169661689467, 842274139270535842409744945935128951705359842639982830775234202022927766509101371734465485773595508746113280, 700418817778098786277078342411520118692346350422606462723911114006419955720829707854379756502697131673319406, 569340337737117832121418471593902796598875993869214230094417664010492029193566188439149404136072598861993782, 311402606048606137904298548604483824215396754817621627161525397920627489469424683846450586021906438112211863, 387556851872999917791805837107172465053410831946704411441234136279016670150248420130484443911023416474044825, 926757025438911433753408433626135280565795754689622472147862347099349687223800534911582014085258437224209910, 1200730550518343100475397485248562827037665594135578219083390443869303562262076428424675489345048272331540918, 853763541787064913980724960667413489272081221293636460056478608052421032518647566798408815952868230194038338, 101239479653925653679074333030959394747942224986065362367651805089673854173857409456735028763240747273162552, 47121618175135904684072490541732295428491460965542084558472179206885868302518875995103252249901230211543525, 982857581226299143840954166901835590289581958403367749920630419874452320611289908335828280671343750955279622, 811158165015249537987500368246254094251025296798974323499510891442047224515941233490537351722658420472211406, 190329661527190452974427725241771623761097473044383743958766087362063693259351495833117766854793893313562091, 50142672419825251936694820690428751885608034385161146860936149367718248528534064819383444639850833791987235, 303074295943054006201261314482928767581154579713194119273091027835447157940166620065183762076400863876771618), (1079372098255337688887136508726900390205048294920188450514628679918679463674406107209346812192726950726526095, 1185407402236867425841849519771446165946457212261250741849109704048981912211308244902430988525473241626691376, 841449701483451008458666118133003457345663684791358742412512477100467235117244326687250726234511967835213312, 947580146274192515572496516072653825873017616320635389497290350126027652146744723140627689652187761111324722, 119701810379427632902947235248083296107591243190851146608219622795996254840540272877119978122901453247704831, 1640347806216480803403265325130213955203137215028089484587105315192029771752510728839945151370945087147585891, 132249802108051544701535447313025681301951421902989862817119883237200082396640574742757738128092983379391192, 222015024534828263520557570979535921258670062891839524631837193227865004386250245701652729081402110107343213, 574045525239164646488552167939702566130627137278663509529342693657266762662320399075679168964197800875153680, 9484269602968566121096790600370029517627994135450856762373752676667516556085799114664479005324973494415028, 1233903272461676350245321015676982196376541150525344451565454505261564207710591321827100801836574162863320101, 1148801053084576503181167454811439762743688828522853724573620157831506900806010782322188583027710897929400855, 1215932391694160648245705883928262594648092322383337933840246087760359598672361289173906269225985279432329413, 1256312697161815430876406109440773985803220898059915842809050363551861707962446265001460104545875429415188571, 872437290854895473828669647489120707661030662446214686039744557281742237010820123691242130056373279816418223, 1152504352689745273833849365904838499734041820598612058887413417408375952316351943382602922195063490977108643), (710963262741981151820936850518208399242203827946566243778081082652103950765186323857775548839335091162334870, 1456629029412002617034972369163460599977456975519008830537020404598366361266406883048353122402136998033965378, 16210930934876839488825850002875991819998003905202118064600427478988072592144130697157997625511415256307363, 270428172771482397506264701557858536676609324837517143183553201495149542640445267791184678417415736435998954, 849877849071009557937204357275192288430487696593090949890966075681654171368216057356945570659434491278721274, 552620920720515058560474932264018680445939377267909570543604994142303109067032086804888256059644299353469259, 1172127755569012152057329884978219429036349809157746825385122333254835103162162825165494896169153369293261353, 411671306380066471819720700550244415062425059661769246453503317934644249097679366952285018648871841314934569, 402751953198228508151317654119142703515415046161021988593791144762527354103153471097112572211022718546278586, 766801594113742202593740150497848890462669867082716753718908389103589627909820578043565509568785779049218055, 797931710812718040702146757192489993108919934337204902859533844054220052514095634360789107051511556938992653, 256266683996681594597141537434560889801561902972841661123996099001842861984074656394526155375881352817334296, 1418258257142479430747867834021373209498823909476696372006454504116466387484456504969162467214870003218548093, 404210566834668025438526175366143398913809348454169783995888818764258941987118278616050245839417646478639395, 1124315278703311203910253162758503257319860043824222656290539806527988308952238570582388061003539053283572317, 31271013457852406387457908247212294447150322908910202024391938488810830594827404698941451758903033151739305), (548040572051344376515276589131924583544500173392618971080814926510006336050708851946164444215551993653085559, 625548909252967533735849839010612868036138065774462061438762751772756816905614389595526904873401107330945781, 1691072562255106837879679641865899852020852750546650376805631545200564107660856702442704801403013254039741569, 1202012272195706005158418331650181482011843322779113997244205689517798278846032040147415770067172225826668913, 150921370600945669819511437694954238255973349434792437308411767994329401311792429847861423651135286847713713, 1081961677217384177165919288637329442102000700465921211931830210416642976436505857583147668075896913252875900, 38632177474960713645129923487571475415432359356662267792821760890850300033591793689594738256015530177371155, 1938890600587173893505401800316209462990331410030406162509017807707491700220029026718794390924558159879325929, 1229683571480518162665771834260511788435892562017987248959417363680402504200735302566356076064181245050609719, 1413469344912570390840315618128490201700779301153932364796221898469284008600385792913106541878951550172812412, 1603029001236324174565529401277703840486413251539616667351366375992862845333710947994522282396247706689372612, 1312758180969033170349160258170632626914169138097284308377628285441990421588369514659056847472785376422032509, 420630504359244172568640650703118406520051803679165798526263777300947905179710846980565379197700977880435719, 1585809275814789433535721083967397645766740283392075276186763802353434721723652579350998943546412586002101517, 589210671463132192681719552822630237990180990772437934057045440386799228059672695104509559337510094293921851, 930311739285308931463277260997251754864363249024137932070462953287695059475197620094345118725029808434080647), (1467336759171283069626565411462398975366496846832073813368207088887535151209170863516635004538662162471343762, 977074540452559328447962038595860262505507375287943059556072116746789487913192871746080153669811094853532543, 248650173456825688417957774461661449303260122768178786152237705032396522955301949686829800599729957124936881, 1575141265084365943986079682243623659177381136848989044089310647747968289751919614920688971461354420388159314, 787447705570464488319993501786605650852712556006717975039783792984896866011280674498846348134268287187830884, 661441381812931924846748272167364237789611518544035906523025481686525617167205320161832280314277716928159938, 713730377306644084040092474766578448161880233899851837176624863065798544631483002502432026196641108684529802, 678127349747227597169480575382795227664094828375789580467264872090685308013465629197529880718542771111962085, 713346890417527875247397732148633974225980066787252539001278528256033329879214523269733008776540235645258616, 247766390946758644831951312737583234549767619079720848362262835109239728499038516392540238454397695238919141, 222705566395366047399107473153762271285577494629225535376316438586692339782315068484531721893605469117790911, 1167884170034239946155932241100371322938666487622727711102849910832028974675686714637275598120136818289661580, 932355528178259401857913753619901059996671717365121827133186058111555002840548732397926137817560930059114770, 1002746708088820961204612547451117005094490428961711590997242233612795804195894564433549670531755192704377784, 1679333740390330063990893123547127749235201034112770813357092856319834835071400803617023235189669738802029304, 392242968045894054394410450448222234277751637234090312939171392505401592465971560873369509814497556456004427), (992468551424268052973878019321034098395629270356898670428754992273976085327043949634823897407999881749733525, 1451715409910944943601462101816705970560866315969026142750871006351008564752030350792755878689749793232050135, 1157009611084371602570908328606510003229611538486635093673400888168806076758399348412361589040924760249605165, 973495747254748476179115555073571696121985220451730406501150178959729503505597527610925614459285006121361402, 658639350805308777150470408771425787492359455148463053354655386025849573731791445060202388386991444927738961, 1971053413102762878789808762083387327923437569500667206884595783469944908304113399563798234198010177066652742, 2115317009351535055976145874152453249874377928041776362924821587295001750589961370153217409957345893981016872, 2234391928340953996585129136832544559226500428847567089886903639518503721330552899247101854148266339819317188, 95072622447945887900832352837970706552989337874284483457123454853555569418515739360750605423996449645105107, 1875846203425953685568066514593452384199151872393675498259844146377412020045792635132008533335688986283672883, 1810914367567014038914603180161768355184164085528312813795257698944266962072856602341302516572423400651692332, 199467426284808218867281478238942162630473707920489559716102969301577891302451826382304815567177368764269462, 1702858806121853895873612873027468484445637308444414982865712291274495592467886617988854786928674988921911946, 974805688584434752190621523541453157436916884469405725317513726173004242595140529349594953961249312833707385, 1563386402665143107620951148197814309632711706132670874925320046005197489375705725978209339748911734754574512, 9176208496797520354591828022203217543780592247378582726844977716549360683455502116572757173493442942031259), (233445330763035713906480406558126679912369584387609168775775009002471869774809156648369750200202982292450110, 1368815767827926042586853692745612271551227815728536321062147470922660524586014022932653135440512072849734316, 384817387960742369820850831236493763489057262900417346331312192757646380527152649103439831363756430268212632, 397496835668788385513140511380523318193705211763259441405319027544230424059467351506182237622329904982387715, 698110549303594315292020493881564774109817641862010152125384093754339939993582331419363730859850611879969915, 1605164779311866241282121191148498603150640021145381378570376215574622721447700807491428199428586193250231478, 183289800466565443527759722034380747076340683994766781001250154775016249854621154061869569618175611639903701, 1150055471085650022911275723850717353026238077245380241936809820048468325748232815290091481729807017284552381, 620603888284975571831631670369627892585626390577575455138594479292012594683550062832525870724842983985770747, 1141328685248613112603867626739876650489649831411725855910037151420885700357073101388703693467739668094282156, 624960745989505135902341328405609018059617712001038139854396706552761169916956343895696631019491737540425263, 563529618847514880940393862944843314371586107587203186648893576096997599582868166110130990825643297466007343, 303984049882076688174095718097426318142423827941965036899905826287812216266056955154997043369442371230205564, 1078658398740303308773443996075991099257452827614150807223915130507432012180318161902329283469259552998132456, 537873127629863133215961576717191616451542237544837768039490490426253210893390806083040946873190554913432278, 169827329251258085772690777190607029224657639816497950869244582534669264355479002364217211861513540611966251), (1096245533475537361190288774520023066028944190947416838212035157548679351561405521968403358714145944584630399, 1279522123404803133336059116798495103535564541817111467998685969195461307732488357939481563472485600907763277, 1621837589082192223743462826999866153643367040938611577504635652882478237855735236683796485402281552828564582, 313242446386229290517631456915969842064339663908557260803068874835492915635010632958561104764179416843832161, 578485247743964493116232317100459206200994787373794324513012647234668115712570705116452853082031543244068838, 219236836922423209713975639747607435338261033480938547612396078378825597472824554607631157060224948270436605, 979376137173103622620811921408735178993536617946054941969002748851996870693909895946038600886242442551160010, 1658962387074248584465660456576639004572633758113833020219450181488960527172176749430939869777912514216215008, 918251986210568868284757564587914989414930967922138557622606681330218265588255276030855013898182774363764198, 416145177416426209139713794767532287475150472389752288032134927843857792069932225643904301155189056410493405, 1346241144466810519932765660177492393372766698799833323172412119406803241967611867883756378782484642242570189, 386044859254038630462329030959102689573511312525928529436140682252354194273696092297158967704938034048108529, 1484764098293658918774711805629994556483924451761564995022607799099721232009570720017552575816071384460602164, 1038730041745536343360704248505932016034663062624529750511404210052634999557834948325392848734950387651599858, 840891087158618754558051176285252692949387956006228734495878738266601769957106869402114856213091762226629917, 154290307227368077749870332568887647430659666317555291698382581129904308224189689828380085709625178546228569), (957542186457140429878719718043221941900755820226325043983141960244787673981451575491224713734494596866261378, 724047722558649330730843109648231137501160718812738945124027170000449368988489179074784908592741358980048275, 859691367287711190756246276405852338601741033988752600016986903642679515575127575700961271435459772059797413, 700326697100002173963353478913834231346709568898840509699454481415437420831870839656574933271416282890802499, 1212799233481683655114268450576868631340238725268953631719891739166990447791141389709487362430025981929525475, 434223116592471574825271824097577518464718630519588487323509231423950783528915761191895287228657263954146704, 217358723385922851738144743498951415510775556931588600580907447804579013546360116371411758271211755732813673, 1298302755143305654862242351853763864348853855493677603188749853805882418947261680899385729883193441043359755, 1068567433966576654450031707464914827557285166837067988549886717564803805511104947509349083926244852733075655, 387252452536150691159164650119964238247624960830148325826046315786865241210396695679059829317531866257898261, 508839717431096857213637104691635167536835851969398382071457470260649594681556257203954946581750028844005177, 1206518168075280470635211428031620060153968523722913415228454624000108732714232864597004081584662635882607853, 648865561108057369649107548455893267620716326822663875048533849791081284682513605169317071254138817423411253, 328899686789173295020724462964824410189118431101862924515424446992402687451336506312251501354303725597785390, 328255320088054790647176014272991149866112991817392189633550739280062827106546437881018772832904512686978965, 106174800100391915811859026646635920353821529620342998961153251213838054034659090497687918002957863429970430)]", "p": "[1865995351449738305568020175407782211399961865380593201418385016005093079577037578689379305647217584283793443, 1697242394344178603938736175613701840668178871025357188746023984007769445558252186408395718968869377260650881, 2022468188670479218398009972496559844211210519349164350277452667428806390007291454178121579812497234805510519, 1834829294267612129864230457016540640249954796220974248612636878892248451710372726854088698756567786846212703, 1405518966688306890692028628042659763908744036265874596824103451217948291402053599048649577166902926927583703, 1306908379818841354811802528108647022225114028771004539878749636527088666316005228226849317157868863492789557, 1616789308818449288058724288899930420024001530178051122904515573455195995874365002006013181396637101496249781, 1253980640197082323669506507875908153359037006012151867601133670891700927532100671469629678831658698780894267, 1903682307023943435426747954611546184832717459394865637878168715826293943923848159869800611686232172365018581, 1456734579850607615224565915938092349853802772768941452254929266785318676489306434153019311316107310595518281, 2086165420905105719392664388281307744562262795619197207857331245823719830703952955965374642455778791010644509, 1726023515056798169515795231206459220148735483137609272433351313501296592963022379572602085340729076332028431, 2321143867752465622995689244649230653121108609695672723739436709976291791473903654863830072020811159448364217, 1654702076906300292576294228173753061411836852146848089290417136859589687837314338726356779964670865195828343, 1907313129296467305635718505435422104472615990939772968829964204948404573958217594528354537082412412899627617, 1320309629971476331896561625690122232816350401607709796615097327024821433804124798985230849347309403103099677]"}

output.txt

{"AA": "[(1189, 10015, 48675, 15975, 31817, 26015, 24250, 18821, 50214, 50017, 75, 28732, 10257, 5455, 32069, 32003, 45003, 39819, 30035, 37850, 39903, 21043, 8687, 50970, 48905), (20794, 45724, 35989, 24379, 7208, 59121, 56688, 17926, 49764, 54939, 39552, 33784, 40662, 41878, 61413, 11020, 48377, 55636, 27284, 46849, 51507, 39309, 31205, 30147, 27390), (8891, 44176, 3116, 28266, 61310, 7861, 60115, 17072, 61389, 28216, 8681, 25263, 23085, 47312, 5606, 27801, 32616, 47700, 33738, 30823, 49772, 5402, 1340, 52348, 58993), (59729, 14749, 37529, 46046, 4920, 50580, 26744, 8050, 55570, 27500, 17842, 37757, 22392, 22232, 25725, 12528, 17681, 8000, 52605, 31240, 61798, 13548, 29336, 8562, 63604), (62818, 3170, 32754, 11215, 25744, 13912, 38104, 5172, 54208, 35180, 55607, 16626, 42687, 25363, 11701, 3901, 8207, 31948, 48488, 11573, 57550, 40087, 63839, 19719, 15723), (52273, 56854, 33393, 33910, 44783, 33936, 50006, 60028, 49899, 16067, 25566, 11597, 39668, 52732, 3024, 27439, 50039, 26424, 64367, 20331, 34933, 37601, 16343, 46722, 1336), (64238, 24453, 64780, 31971, 14105, 9730, 55314, 64004, 27281, 35422, 24395, 21198, 65439, 36958, 63153, 32784, 53301, 27430, 38742, 12846, 62864, 10713, 6909, 27043, 59107), (37610, 25432, 44610, 7077, 32903, 46884, 424, 23310, 36950, 4672, 26311, 4134, 60778, 57046, 62145, 13373, 61257, 57634, 33850, 32777, 3813, 34086, 58147, 18906, 49309), (59705, 30936, 61109, 21077, 49611, 20689, 6512, 20992, 35917, 8675, 18204, 30551, 2962, 36546, 56258, 53604, 29277, 63461, 14239, 63156, 26182, 45023, 19121, 21590, 14042), (63345, 60395, 30249, 54797, 22971, 53638, 45089, 5737, 50861, 1615, 7745, 7453, 25322, 10013, 9169, 48005, 65311, 61522, 41889, 65084, 25635, 52713, 9209, 51490, 45475), (2749, 8590, 49969, 52657, 36740, 11611, 39325, 59332, 4772, 20837, 49963, 52870, 49573, 14177, 34052, 51096, 26262, 669, 32596, 50328, 46253, 10664, 15017, 5469, 29587), (59594, 31977, 45606, 35783, 9846, 28769, 17791, 21444, 65356, 217, 1122, 51359, 64757, 12133, 29430, 6393, 22444, 17366, 61872, 47809, 42245, 5572, 54609, 50011, 15060), (54153, 59275, 22418, 19462, 285, 58937, 10415, 42536, 13880, 25909, 34947, 27477, 16119, 56351, 8650, 55100, 58424, 24098, 26924, 55766, 19002, 30119, 17349, 28884, 34024), (5900, 49521, 36902, 20406, 57851, 51299, 41603, 7915, 45259, 33933, 27106, 53886, 14958, 4865, 33344, 51406, 32415, 8015, 45647, 19083, 60188, 37968, 39697, 46185, 39218), (38952, 55178, 48419, 47334, 44855, 51768, 35749, 11544, 25826, 48403, 3166, 60905, 28119, 14824, 55122, 36964, 1615, 36166, 4075, 33143, 24879, 59618, 58514, 44750, 28773), (64561, 22819, 8135, 20029, 13338, 48351, 59271, 18434, 27753, 41685, 19274, 43772, 44806, 35061, 39441, 19719, 48228, 22571, 44298, 45194, 22885, 48082, 42131, 65306, 8463), (12767, 5415, 58017, 23812, 48236, 54213, 35283, 8251, 46681, 23031, 19179, 30985, 46917, 45270, 58973, 23415, 10282, 2702, 31577, 47355, 28461, 38212, 14595, 15208, 1648), (37521, 48562, 51345, 56722, 50929, 27913, 27658, 31149, 41608, 45971, 49939, 4274, 15391, 31038, 37515, 37228, 27125, 17032, 45011, 55555, 36759, 45464, 53475, 30184, 41318), (18405, 53048, 40180, 53547, 14826, 24617, 62340, 30899, 51386, 15970, 24481, 33994, 10935, 2388, 22561, 27227, 979, 33956, 59469, 32633, 38421, 52969, 44228, 2457, 13279), (53755, 1191, 44720, 32125, 25207, 28056, 63746, 28210, 49219, 64276, 42315, 43245, 39917, 16763, 23644, 36518, 29708, 15962, 2903, 5470, 22374, 9163, 64824, 59128, 38235), (49029, 49355, 12072, 53296, 39533, 31956, 19436, 60040, 42794, 22320, 56603, 14705, 26792, 39027, 16086, 53646, 9212, 47035, 21225, 16382, 12414, 53774, 16357, 24971, 46005), (60961, 34411, 26246, 40253, 58966, 61483, 48631, 48495, 59314, 29588, 28734, 21734, 21504, 2784, 6302, 57415, 43851, 54560, 17437, 40932, 61615, 51417, 48661, 30311, 51102), (61544, 53894, 2859, 9261, 22614, 59926, 36388, 4567, 31634, 6584, 11934, 909, 38644, 15050, 53300, 28488, 62550, 29049, 22195, 50873, 15564, 54009, 1478, 13428, 9145), (46419, 29156, 59679, 41979, 53194, 57408, 7575, 58563, 17202, 41640, 40217, 26776, 5967, 39283, 49698, 23519, 39532, 39447, 62562, 4054, 58126, 65010, 45471, 19836, 23237), (41376, 36392, 19809, 27103, 49777, 44334, 15650, 60198, 63803, 9526, 10968, 24203, 31417, 35908, 57491, 50411, 42059, 16550, 3622, 34719, 59948, 59493, 51674, 15016, 61116), (60917, 25045, 47964, 36966, 32799, 29830, 16873, 46700, 31038, 47603, 26419, 64721, 4308, 27321, 64761, 16960, 852, 20569, 22674, 195, 50338, 10897, 30541, 27368, 17336), (16086, 53709, 42690, 17394, 36943, 34642, 58049, 37847, 64058, 24727, 35345, 54732, 46452, 45738, 58450, 12057, 34214, 33740, 35651, 19284, 61643, 56416, 58701, 62087, 42011), (34826, 63713, 19350, 50850, 18550, 59239, 25732, 2020, 30369, 32049, 40105, 51435, 29021, 56535, 3432, 10731, 29324, 63256, 34699, 51845, 41535, 56049, 59295, 39883, 6911), (22807, 8740, 19862, 19169, 33019, 47892, 42482, 41262, 58435, 4892, 52040, 22938, 24592, 63989, 44473, 38782, 52940, 11598, 12639, 28560, 61610, 31395, 14651, 35852, 58419), (43257, 57644, 6122, 23183, 25662, 16235, 58736, 33686, 62573, 29569, 28556, 38839, 11432, 534, 42490, 19287, 17843, 55879, 23186, 43763, 31409, 849, 34135, 35126, 57341), (27779, 24005, 49611, 64975, 62775, 39305, 8490, 21370, 40109, 61420, 21895, 26749, 20303, 54286, 11468, 51973, 1635, 50706, 35698, 64949, 62716, 53567, 14115, 19032, 694), (35318, 2659, 57515, 7332, 40279, 62339, 28636, 54671, 12911, 51113, 4753, 7568, 51696, 7480, 62069, 62169, 38477, 40065, 63635, 45087, 7336, 8949, 29661, 26512, 1408), (61778, 18372, 22916, 6421, 23075, 20384, 22924, 27725, 47168, 64944, 14721, 28032, 33492, 25969, 32179, 11111, 15362, 46787, 40104, 62498, 60748, 56007, 30557, 51383, 49402), (44507, 22297, 15626, 11138, 16243, 34975, 59593, 29742, 28338, 7152, 3361, 39687, 3100, 3899, 64632, 40184, 20990, 53437, 9967, 24828, 12958, 59996, 36130, 61328, 49741), (46419, 8775, 38978, 25207, 49714, 33095, 61362, 45982, 2980, 66, 7210, 36122, 61835, 14814, 63472, 51343, 57338, 19357, 15635, 61860, 20688, 51655, 24199, 40564, 14126), (36094, 62752, 62745, 671, 54792, 35251, 32569, 29945, 61833, 28101, 42665, 19473, 40919, 17448, 40478, 25718, 49028, 55652, 25081, 3836, 49942, 6671, 47646, 54503, 46628), (43021, 29427, 12640, 20309, 28712, 6921, 52820, 25287, 13171, 29863, 6148, 18846, 39304, 12660, 48191, 37007, 65429, 64575, 35424, 16317, 36733, 43015, 5976, 2348, 20529), (26396, 22225, 47971, 27284, 61466, 18856, 11275, 55373, 23257, 47561, 22340, 34273, 64321, 59056, 40976, 45388, 33707, 54272, 21138, 36293, 6887, 29576, 57913, 5683, 52878), (35322, 49931, 39571, 12911, 10564, 13215, 51929, 48907, 31753, 49800, 52523, 43658, 60805, 45781, 31078, 59931, 50406, 48612, 9262, 52380, 12869, 44495, 37759, 35238, 64654), (51744, 23690, 61871, 40623, 56836, 47970, 52786, 3677, 53133, 14507, 65141, 32996, 11637, 917, 567, 4072, 50318, 17295, 756, 60530, 3513, 27806, 9362, 49621, 17465), (28912, 24557, 47100, 49673, 1840, 39141, 28867, 62941, 56031, 35779, 32658, 28476, 35210, 29027, 43279, 45177, 17684, 6605, 19589, 42506, 46170, 25807, 64243, 62907, 49740), (62693, 12022, 31061, 29880, 59706, 8593, 54752, 61927, 65091, 50452, 31285, 44448, 48296, 25513, 29515, 19206, 60356, 3724, 11054, 33890, 2075, 3182, 6513, 15992, 23389), (37048, 24550, 53143, 64535, 5484, 50995, 36812, 49481, 39082, 55441, 42268, 2179, 63279, 40520, 38, 25575, 49328, 19231, 11554, 55024, 32685, 51805, 31044, 5213, 60012), (58493, 26844, 55535, 11896, 53877, 230, 14124, 43884, 61059, 25080, 63582, 41528, 4167, 32497, 50901, 24647, 60267, 56582, 18928, 16462, 37992, 20417, 31843, 28987, 11501), (32947, 39920, 22571, 48651, 2491, 51179, 43149, 17170, 51739, 17402, 2117, 23149, 13252, 65479, 24840, 14658, 46214, 5365, 8979, 22938, 63016, 11220, 21817, 36473, 47998), (1033, 7295, 33096, 15709, 6470, 26664, 26961, 17754, 48988, 6944, 61031, 59519, 24613, 18224, 59805, 34045, 53322, 48966, 6215, 63013, 37270, 3702, 45911, 18471, 41793), (44049, 52929, 22215, 40602, 55329, 59732, 45509, 56877, 21911, 4007, 39188, 27720, 45269, 19329, 7566, 44285, 11421, 6887, 45138, 47046, 38229, 57521, 19116, 55114, 11116), (14015, 39772, 32331, 35406, 49627, 24421, 592, 50328, 60751, 47704, 63152, 26872, 19622, 40431, 16318, 47335, 41746, 47762, 49605, 59460, 12533, 30479, 15090, 38698, 59449), (44029, 52891, 38354, 37813, 37020, 57441, 54459, 60842, 17425, 51577, 316, 38017, 59380, 5239, 38384, 19661, 50345, 41230, 39509, 8401, 65229, 54097, 53578, 32693, 12734), (58852, 33428, 280, 20439, 15757, 41997, 52470, 60567, 63969, 50724, 6995, 64357, 23787, 26807, 16690, 65509, 16946, 42181, 15672, 22593, 18573, 56922, 17055, 34481, 39070), (4258, 1875, 50905, 65155, 60637, 59925, 60381, 45498, 58783, 707, 3011, 55554, 27993, 33427, 63501, 44797, 54992, 34007, 4394, 48782, 59888, 5892, 45084, 43044, 39549), (47800, 45880, 38963, 57213, 62669, 63292, 29216, 16951, 28952, 32098, 25444, 49971, 41892, 37988, 61714, 10615, 21529, 5874, 42354, 33931, 5770, 55071, 22008, 15321, 48563), (7666, 63315, 27867, 38191, 51517, 34526, 8705, 45915, 61406, 37274, 30932, 19538, 22988, 843, 10899, 16471, 55748, 11337, 60897, 1151, 47726, 20191, 27764, 33011, 281), (44491, 56739, 41425, 47202, 52342, 23378, 63825, 6633, 11898, 32141, 41201, 50496, 4966, 37384, 29162, 27943, 46501, 32712, 54328, 3898, 16830, 52100, 22176, 21840, 7099), (36547, 50240, 51608, 59796, 17285, 38400, 43056, 3033, 33641, 29543, 8347, 30294, 55755, 57125, 36192, 45853, 63701, 43882, 54613, 52197, 38572, 736, 1753, 33176, 10888), (17126, 14777, 49957, 11609, 2260, 57808, 1505, 42332, 7819, 22706, 49046, 49187, 3105, 36193, 29855, 47703, 1667, 12235, 58881, 39267, 14025, 18957, 16677, 23494, 20531), (65126, 4463, 29789, 38411, 42426, 64920, 13285, 1069, 28747, 21619, 17200, 56729, 39609, 26687, 1870, 46670, 64502, 47955, 45636, 32500, 62260, 27511, 46195, 44502, 64638), (22953, 15164, 46166, 40119, 9342, 17289, 8942, 44913, 55593, 34458, 26211, 20373, 57136, 27022, 17417, 4428, 58718, 16575, 29576, 25699, 32528, 64101, 3629, 50773, 12475), (6281, 33672, 13970, 51347, 7111, 59686, 29700, 65236, 13373, 1667, 38767, 791, 17028, 10850, 43187, 52400, 45239, 23128, 5190, 14282, 62990, 48007, 48210, 62375, 21723), (57871, 8903, 65120, 6023, 42084, 37817, 56778, 3838, 37299, 62112, 15304, 11160, 57614, 4333, 32146, 8273, 7681, 50186, 52355, 47884, 15351, 25092, 34186, 23518, 64604), (31207, 38513, 62642, 61622, 1055, 51323, 58740, 32182, 3913, 25882, 25263, 16810, 1280, 53505, 24807, 49426, 5486, 26362, 19982, 35555, 22541, 35060, 52809, 32532, 37624), (40577, 33733, 18676, 39922, 31732, 26761, 12977, 46375, 62675, 10345, 62268, 15946, 39764, 17015, 40324, 42457, 45383, 1015, 5396, 34510, 63481, 33456, 29458, 20949, 1599), (61540, 29175, 63557, 5405, 57593, 3846, 5442, 26745, 13537, 47100, 64065, 34056, 143, 29955, 29987, 8459, 35854, 48752, 14759, 24859, 33300, 61949, 954, 40980, 15608), (25209, 60170, 34259, 45675, 28885, 27034, 13603, 53924, 23568, 9217, 28915, 26783, 65338, 7518, 33357, 1146, 56433, 20112, 32451, 7959, 49350, 34694, 3240, 22514, 31827), (49018, 49762, 54715, 41874, 30640, 32419, 36736, 26242, 18587, 54536, 18194, 31589, 48986, 10622, 6150, 12689, 55556, 21808, 13106, 14561, 10137, 59467, 58344, 55524, 20716), (59760, 12330, 4736, 32604, 22399, 3209, 22257, 10063, 56794, 61560, 9386, 1316, 8713, 38511, 54391, 64128, 31262, 12402, 14926, 10065, 57568, 18716, 56893, 50431, 38452), (41775, 43406, 15840, 26889, 52878, 14767, 45258, 44226, 46316, 22753, 35617, 30370, 61519, 17456, 51855, 57899, 44411, 36646, 26232, 46923, 32210, 31101, 57918, 31491, 48305), (31932, 8195, 20264, 22185, 12341, 32450, 40468, 40194, 5236, 15393, 23692, 26274, 44912, 23664, 39876, 6288, 14416, 47884, 23942, 21356, 47045, 2355, 7174, 55793, 5899), (41179, 43376, 59022, 31588, 63752, 47138, 59457, 17939, 44100, 50900, 21604, 3241, 50463, 16341, 995, 55792, 8171, 6173, 62050, 60712, 8716, 57675, 471, 51461, 52279), (60906, 35728, 12887, 7680, 15544, 33531, 38108, 33929, 38830, 32916, 61235, 43886, 44066, 33046, 49859, 51975, 29168, 26073, 7855, 1682, 7697, 53757, 5100, 20482, 12294), (20744, 62533, 32040, 32864, 34801, 38760, 12455, 59871, 47787, 55564, 37671, 55868, 4038, 23412, 4161, 8945, 48324, 21462, 53808, 32447, 55560, 52403, 6204, 16074, 25759), (62136, 59381, 56589, 20239, 32177, 17307, 2162, 39791, 62888, 65094, 55009, 18557, 445, 40699, 43117, 14984, 2503, 36601, 3263, 3117, 56379, 57234, 62303, 21544, 33527), (49420, 33908, 51697, 31351, 39412, 36749, 15400, 60266, 24219, 33971, 38693, 15254, 36910, 16958, 11124, 62317, 7172, 37531, 39852, 21372, 51734, 24247, 8349, 18451, 31683), (11290, 57344, 20620, 33350, 22734, 46032, 62460, 10717, 14455, 45269, 38724, 1088, 39797, 48599, 27154, 30079, 53063, 26217, 11728, 27377, 22768, 33007, 18338, 30332, 35422), (27810, 54576, 31210, 37790, 49868, 51271, 53119, 56226, 31321, 41885, 18631, 33718, 6319, 31291, 23157, 17316, 64768, 23388, 41674, 32586, 26816, 11418, 50941, 11395, 20161), (14924, 11414, 980, 45398, 42331, 14658, 46974, 19201, 33329, 32736, 49787, 55325, 11785, 58637, 24957, 18789, 16678, 9732, 41963, 9221, 14904, 36059, 5322, 26555, 23280), (31960, 27764, 60888, 41252, 40017, 54501, 14889, 35216, 23078, 14200, 35821, 54519, 26086, 18133, 59219, 480, 24325, 40260, 37716, 51049, 24763, 620, 31828, 25187, 46109), (45544, 54064, 1155, 11568, 55850, 47596, 49554, 37128, 32113, 25839, 59323, 3306, 48313, 29777, 43114, 43218, 31951, 19636, 41033, 48677, 37912, 4439, 52672, 45945, 61273), (6583, 15612, 56560, 27457, 37885, 811, 27472, 35620, 23307, 47595, 12821, 37839, 2295, 3148, 33868, 26635, 55788, 1902, 10752, 10522, 56669, 59010, 667, 35734, 3302), (47602, 362, 40408, 20685, 33561, 48382, 2602, 28508, 59065, 41452, 6471, 56497, 55740, 45242, 15009, 8004, 45641, 60657, 23504, 23392, 56348, 55434, 31140, 57807, 44624), (11574, 33546, 6425, 24309, 61960, 547, 61735, 44861, 6394, 35242, 61500, 62210, 8161, 33717, 24827, 20736, 6109, 36710, 13108, 47615, 2365, 23469, 50554, 33929, 10213), (38514, 11905, 9818, 48320, 7648, 15444, 31945, 7820, 39340, 37854, 64397, 24218, 22594, 19014, 870, 30798, 23310, 29514, 62976, 12858, 7289, 54096, 26351, 46809, 5704), (31863, 8845, 31045, 18400, 33116, 53627, 35080, 22970, 2674, 59192, 43938, 31962, 56161, 51886, 52096, 15059, 47933, 20121, 61878, 1658, 63622, 18800, 49684, 38180, 13948), (55875, 10322, 45271, 38967, 39026, 40012, 7690, 46309, 17709, 30357, 56975, 15716, 24265, 6937, 15201, 8204, 40586, 6204, 9783, 65197, 47792, 11948, 28125, 63292, 623), (24258, 53571, 56730, 33791, 22863, 31834, 25850, 65322, 2867, 47206, 17379, 60559, 14113, 59729, 58067, 40837, 16440, 31203, 21282, 30949, 57561, 34713, 43238, 10328, 35991), (34961, 24798, 1480, 43232, 27933, 50909, 14501, 20690, 33991, 31459, 18322, 55750, 23286, 43000, 62349, 9101, 37568, 49874, 55500, 59424, 10515, 8170, 35689, 19390, 12676), (23767, 49835, 15539, 26257, 39179, 55785, 5614, 38587, 16929, 4026, 19696, 28503, 57066, 22454, 5027, 43182, 3245, 53774, 44590, 6508, 33713, 52722, 25326, 44262, 5171), (24630, 46000, 44776, 27926, 62198, 6858, 43391, 402, 30017, 43391, 30978, 26976, 54914, 44273, 39785, 12178, 10762, 22018, 47653, 34252, 41764, 19470, 34404, 28501, 53312), (27703, 64263, 30241, 62133, 20977, 7576, 63936, 31824, 23898, 944, 58873, 12088, 29477, 5183, 54045, 11336, 18024, 59893, 31274, 13946, 17506, 6000, 40409, 7813, 23687), (10846, 55583, 21891, 45062, 28668, 21070, 61955, 58729, 2999, 64957, 16401, 49269, 25283, 57011, 6817, 34021, 45700, 9433, 55562, 35313, 64081, 22759, 12313, 37994, 12354), (46908, 61208, 21549, 36717, 47801, 25502, 17436, 11717, 27258, 60403, 17176, 62643, 47511, 6568, 51014, 1359, 10202, 64019, 38271, 13682, 6991, 60060, 21187, 6808, 8308), (2522, 40767, 18351, 34686, 41850, 26592, 20099, 4596, 7264, 43184, 65107, 6807, 24395, 31384, 58845, 41893, 39376, 31013, 26578, 30904, 8544, 38937, 29885, 53250, 43138), (11430, 25113, 10732, 49353, 54369, 9622, 8053, 50345, 12686, 19757, 39378, 40728, 58021, 60258, 38064, 47680, 60532, 56982, 5432, 33250, 951, 28976, 64551, 52352, 25121), (60151, 22317, 59487, 17393, 29261, 41470, 33925, 1898, 49703, 23814, 27357, 57173, 41835, 21588, 44686, 32544, 58418, 59456, 52458, 60669, 28896, 59545, 45667, 54902, 12351), (39983, 63788, 2900, 29247, 25359, 53575, 29078, 65393, 24080, 27200, 46267, 21854, 20164, 42105, 16435, 28613, 45919, 54966, 28981, 65223, 63064, 26992, 36997, 41605, 6976), (15500, 34867, 50495, 29389, 55660, 21194, 1822, 52615, 51842, 61201, 35680, 22971, 2629, 1890, 22358, 24604, 17905, 38551, 39103, 3036, 65139, 51662, 11973, 60710, 64773), (38500, 27088, 47974, 12887, 30022, 50699, 58037, 29612, 64140, 12208, 21887, 54465, 14381, 3719, 10848, 39152, 49050, 42917, 14671, 3088, 48870, 27616, 42935, 19636, 22425), (4890, 47931, 42696, 21026, 53065, 63018, 27022, 14329, 14887, 50745, 63957, 5828, 58542, 29718, 38148, 41826, 61722, 62179, 5349, 40926, 44925, 54125, 31089, 982, 3246), (56941, 25301, 36482, 58770, 26231, 39551, 9758, 24846, 61039, 36742, 22094, 51029, 53396, 33273, 20989, 55246, 5190, 35667, 39283, 15560, 2424, 39178, 7610, 502, 61668), (45955, 64649, 57091, 23326, 30513, 52722, 22456, 25636, 59178, 61951, 4600, 17039, 63795, 54564, 63825, 28934, 40751, 57808, 13007, 41406, 59819, 56352, 62022, 63436, 4496), (38991, 27726, 30784, 61933, 59633, 6981, 22, 61572, 31857, 63602, 34143, 46712, 27497, 27736, 25125, 31324, 34009, 8349, 35433, 5002, 42784, 60860, 18768, 25631, 57072), (59036, 64992, 59070, 22401, 47588, 6986, 17938, 4462, 36225, 54626, 17833, 26335, 5219, 11314, 18744, 10801, 33623, 28413, 39095, 15729, 49249, 64799, 14711, 44422, 23661), (50577, 49517, 45107, 2003, 2578, 2448, 9961, 36675, 2871, 59923, 6620, 42295, 13897, 16128, 47243, 19572, 49484, 29328, 52898, 58744, 22900, 39176, 4831, 52660, 21535), (47256, 5116, 4297, 62579, 14968, 9674, 28051, 34737, 18568, 60931, 15044, 60714, 27944, 64681, 51273, 48485, 44973, 42499, 14256, 60956, 37783, 22616, 30113, 28339, 15223), (15658, 45438, 27030, 44854, 1254, 52651, 37189, 2959, 60247, 18336, 58405, 63846, 60392, 53945, 45997, 62580, 51488, 24983, 50331, 51126, 53320, 53885, 32972, 17324, 464), (16355, 37700, 17527, 24445, 14604, 4654, 37393, 46292, 15379, 54510, 31120, 23868, 28267, 12078, 13973, 28581, 33010, 10613, 38960, 2573, 26949, 64948, 46690, 24233, 23032), (1887, 64933, 29753, 38644, 46928, 21001, 47120, 57250, 39069, 60845, 15932, 14914, 46297, 1721, 51279, 39630, 43716, 12441, 38389, 143, 65358, 36523, 14392, 37640, 30380), (25481, 39140, 62717, 21583, 46470, 21758, 13338, 4255, 58299, 23091, 33226, 3860, 26889, 48949, 49793, 9383, 3938, 16099, 40421, 39022, 31454, 43500, 58488, 63728, 25075), (46697, 38622, 52989, 26121, 19587, 48206, 6388, 38920, 56593, 3667, 51564, 13608, 62171, 43786, 14880, 5709, 22048, 58228, 6008, 53677, 13325, 5874, 6131, 621, 33004), (48311, 46271, 11438, 47367, 14229, 37620, 8542, 56905, 16562, 57503, 64873, 39978, 5037, 51789, 6427, 4571, 9452, 63563, 921, 47551, 54173, 43863, 27574, 32684, 15168), (10750, 65112, 55772, 48980, 65125, 19230, 33247, 22789, 54209, 13356, 10726, 53229, 15018, 49679, 39109, 64282, 26720, 36376, 48420, 37427, 46543, 28156, 458, 57450, 55038), (21790, 17739, 43411, 6198, 13795, 34492, 46749, 36992, 59189, 61949, 33808, 19569, 59362, 26166, 62372, 22094, 52647, 13589, 21635, 18821, 54718, 57728, 26270, 40682, 25371), (2, 24573, 14402, 12875, 52743, 28860, 46402, 11996, 17939, 20762, 25882, 50582, 30869, 13478, 8913, 54608, 16803, 2650, 16470, 63451, 29753, 31845, 63017, 48074, 51680), (46273, 44706, 9367, 17509, 34524, 7436, 5248, 26773, 40395, 61715, 6949, 44716, 25629, 49605, 36784, 56697, 29968, 36952, 50060, 9912, 21533, 53079, 49279, 50264, 37715), (31119, 17015, 43118, 34860, 49113, 63960, 7648, 44282, 29967, 27990, 49105, 36321, 16465, 33104, 54481, 45810, 11618, 36971, 49837, 20655, 23679, 49667, 37948, 6962, 2423), (13345, 51212, 11335, 44015, 56326, 35100, 8690, 54753, 51413, 23009, 47453, 63381, 13897, 17266, 46005, 29189, 15568, 64486, 2238, 19229, 49532, 41128, 13917, 12795, 29964), (26527, 48890, 16051, 27837, 23979, 56510, 64077, 1769, 63022, 35609, 64783, 32770, 14041, 57732, 9942, 19357, 62592, 19753, 44636, 60598, 18488, 15705, 26966, 490, 61251), (62129, 5327, 11284, 49790, 19148, 32420, 35448, 35688, 39647, 59442, 5312, 41868, 32015, 14723, 63712, 54547, 27902, 56674, 33958, 20071, 28477, 10310, 38093, 62848, 57982), (21417, 45979, 55689, 57192, 11998, 31573, 22900, 15552, 50550, 11213, 13159, 55202, 949, 19090, 63947, 47013, 54188, 54409, 1831, 1417, 7477, 29238, 13250, 62086, 23298), (6365, 21620, 52484, 548, 44802, 55191, 2183, 28772, 37477, 33684, 16630, 53340, 34614, 22639, 46170, 37917, 59249, 3976, 16136, 4952, 45850, 60937, 58712, 2672, 10184), (51843, 13570, 60205, 13755, 9356, 37438, 42268, 59424, 43700, 35541, 9387, 59770, 30162, 53631, 2874, 54916, 54697, 27888, 45975, 17306, 5361, 10039, 11324, 47882, 8125), (3903, 3529, 9237, 21707, 16154, 54194, 4646, 15685, 26628, 9247, 21401, 47742, 14912, 15561, 50069, 50572, 16338, 46281, 58048, 14891, 37746, 9667, 12857, 7355, 63226), (37185, 14011, 37646, 15052, 50449, 44716, 11773, 36588, 32502, 52759, 24230, 28284, 729, 59297, 53332, 10315, 3025, 59663, 30642, 318, 18288, 16822, 9809, 22029, 32709), (37052, 15035, 44022, 20314, 43252, 13065, 9670, 55590, 63456, 39718, 10528, 17391, 28881, 52461, 34551, 47153, 6621, 702, 40, 40748, 5168, 3912, 57443, 23282, 29028), (21868, 44234, 15108, 4882, 26849, 53607, 18328, 40632, 46021, 23037, 13917, 40278, 12851, 57985, 20285, 16101, 40554, 3542, 4146, 12473, 26115, 37025, 27608, 65151, 16183), (689, 10992, 40723, 8520, 21176, 39019, 42296, 5766, 4262, 27969, 27622, 17638, 49095, 21547, 16205, 59984, 60809, 12294, 57604, 15460, 52426, 40337, 47431, 56864, 48610), (41349, 20290, 20093, 36447, 13023, 19213, 29555, 21866, 7959, 15722, 59781, 23215, 55135, 54993, 762, 23978, 43471, 14877, 5450, 8823, 60439, 53793, 38113, 52597, 10613), (60004, 48600, 38055, 53266, 2239, 45101, 14562, 56058, 22769, 34856, 43069, 21170, 12164, 6159, 60534, 56317, 50748, 53747, 54160, 52837, 41518, 28595, 26609, 5019, 31754), (54993, 37810, 44612, 24956, 35693, 46729, 35200, 45087, 44646, 12973, 4996, 38485, 28662, 21625, 24060, 26138, 43365, 61688, 17282, 12399, 43370, 46646, 61654, 8277, 60707), (47305, 42503, 29161, 23817, 18244, 63054, 35011, 34863, 19519, 57132, 1798, 3587, 50194, 28019, 62819, 34290, 42888, 15937, 56994, 52387, 10733, 57404, 4653, 15709, 49695), (50753, 32360, 12260, 64160, 53263, 48934, 59204, 63449, 29227, 47692, 18865, 10695, 4176, 51655, 63210, 18482, 6483, 4912, 22234, 38249, 11112, 63955, 49850, 8447, 21918), (43821, 24366, 55701, 15894, 5393, 59354, 59073, 46463, 41196, 40231, 12631, 12135, 42302, 5928, 337, 62275, 60594, 59580, 15803, 7944, 7169, 19807, 4469, 57579, 39026), (11736, 19557, 57341, 1675, 26652, 39128, 61467, 30135, 20264, 36551, 16104, 61716, 51718, 19479, 29315, 39188, 10777, 24811, 53709, 19531, 7346, 50374, 32322, 2805, 215), (43143, 268, 58101, 46773, 4522, 26032, 3973, 39357, 38081, 58733, 3415, 31719, 35713, 40073, 64118, 34582, 41330, 6028, 45748, 4561, 59839, 64992, 44437, 41621, 63118), (11822, 15688, 55019, 29794, 40154, 10567, 48700, 17056, 48001, 35882, 10800, 10566, 59714, 39598, 37599, 30652, 8587, 2154, 29101, 4140, 65323, 21019, 41729, 11535, 17703), (65466, 28762, 2675, 48244, 18893, 29255, 64651, 33843, 38688, 8189, 50214, 31683, 52273, 33390, 47096, 3696, 25433, 52219, 40115, 49717, 56077, 31995, 46708, 57882, 25178), (60573, 11376, 41467, 33940, 46107, 18848, 28730, 6184, 49925, 15927, 28552, 18569, 36265, 35104, 50227, 16447, 34109, 43489, 30662, 25947, 42608, 46143, 40230, 1033, 47754), (40350, 42944, 54500, 13453, 63371, 54415, 53888, 45999, 48543, 2471, 25628, 17997, 11409, 15531, 45796, 39659, 9373, 13640, 44408, 21993, 35855, 26046, 60782, 20833, 62842), (65028, 25670, 48366, 48130, 8316, 37983, 52619, 44778, 824, 55331, 62647, 42551, 42016, 22032, 14080, 33979, 16718, 64104, 3636, 24609, 30941, 18414, 4917, 2909, 55065), (40890, 36529, 63797, 5496, 62595, 6997, 2958, 47080, 38311, 34519, 44360, 34016, 30097, 16456, 3951, 25711, 2732, 41412, 62550, 44487, 41189, 60044, 28827, 10701, 36779), (22237, 54647, 44861, 28678, 51579, 1770, 52158, 31676, 16390, 48019, 34582, 37775, 11377, 56088, 32469, 39684, 9087, 8956, 44310, 34763, 6366, 12385, 52953, 48994, 10409), (55616, 62767, 50898, 63462, 3543, 28074, 50374, 54156, 5418, 56396, 62662, 53186, 29349, 14819, 19002, 44406, 36054, 1485, 25235, 41490, 44526, 500, 37866, 5828, 15471), (26832, 31976, 2084, 15062, 43893, 51714, 1777, 9176, 19539, 42023, 24186, 13795, 45907, 65253, 37868, 15628, 42579, 18722, 19105, 21260, 40603, 60266, 47298, 4460, 36071), (21719, 26951, 64384, 2132, 53088, 13132, 62940, 50460, 10516, 55411, 1758, 24845, 54841, 57079, 56731, 56764, 26606, 10813, 12673, 6906, 12182, 13224, 46131, 62680, 42668), (15852, 23354, 1308, 25192, 60710, 39038, 16095, 4955, 62978, 33997, 22639, 51031, 13416, 60604, 45103, 14622, 53903, 59220, 17323, 37949, 6405, 37651, 6014, 17322, 21123), (6563, 14917, 49972, 58362, 64979, 24731, 35191, 29030, 32793, 44462, 13251, 12937, 4926, 53609, 8762, 30171, 24097, 22315, 63868, 32159, 51036, 65524, 38289, 6917, 59659), (7753, 37615, 24528, 9982, 60887, 47577, 32025, 2383, 55857, 61048, 32953, 4803, 49168, 22891, 14580, 23152, 13598, 32470, 4859, 24616, 42021, 39527, 31212, 25294, 39905), (11971, 46288, 50315, 7553, 17548, 56280, 18364, 59994, 20454, 20513, 40749, 9857, 50241, 9080, 7636, 13742, 5526, 13445, 23824, 45944, 11435, 563, 12888, 5217, 49263), (25298, 56789, 64354, 51543, 5218, 29948, 36896, 31789, 38076, 55659, 26511, 12706, 19351, 43263, 53305, 63472, 63142, 10130, 47146, 35688, 13690, 10093, 27704, 36080, 63557), (13681, 10624, 18990, 62410, 12498, 41572, 37012, 8426, 14195, 16326, 16853, 2139, 26531, 32405, 7853, 10932, 61893, 4722, 54321, 10735, 5881, 587, 2940, 62155, 18849), (13387, 47370, 63812, 33792, 58978, 33891, 40030, 59705, 51481, 25121, 26179, 36727, 46754, 38675, 39033, 15423, 14913, 4492, 30617, 23760, 12686, 63261, 32106, 23205, 14719), (51689, 31129, 24334, 53841, 6402, 43519, 28676, 20731, 14116, 12402, 52858, 58964, 17431, 41357, 7484, 56929, 28203, 21573, 8239, 59125, 40420, 50746, 48851, 46182, 7472), (33759, 13180, 61857, 44161, 39785, 2407, 13390, 50930, 52209, 39019, 33280, 29974, 51760, 49754, 63668, 17554, 23466, 40786, 60674, 34122, 30870, 1846, 37251, 56741, 53215), (12013, 5634, 63034, 18046, 31162, 39531, 55354, 42913, 7190, 56639, 44622, 3893, 9014, 39720, 36859, 35309, 19915, 59809, 21268, 23049, 4400, 38391, 41722, 5113, 11063), (27790, 50670, 39382, 19520, 13030, 29137, 22313, 22686, 41668, 18915, 43918, 32143, 40063, 45818, 1568, 26587, 27219, 6256, 19819, 7149, 43359, 34307, 55464, 20489, 56888), (43985, 29761, 19983, 25501, 6795, 63727, 20427, 53990, 33829, 57274, 39582, 30265, 36033, 32052, 20766, 31612, 53458, 45566, 11712, 56761, 31457, 13928, 41597, 28588, 43494), (37295, 52920, 53779, 7505, 23246, 56869, 59012, 35903, 44740, 57007, 57475, 3357, 59708, 55846, 65051, 923, 57563, 47603, 63010, 61825, 30122, 33295, 5130, 50210, 11487), (47891, 35045, 33943, 62526, 439, 32300, 39573, 54601, 63415, 27563, 26557, 25355, 28399, 8840, 40894, 19715, 26090, 27554, 53860, 49247, 58938, 56360, 45266, 57580, 36123), (6083, 64562, 35185, 64708, 20918, 56066, 45010, 190, 35893, 35706, 25398, 21744, 59159, 4860, 53017, 38968, 40552, 38943, 42684, 31593, 62997, 30752, 23036, 33353, 3167), (37572, 33478, 36632, 23123, 25117, 51523, 4424, 11604, 5773, 11377, 24038, 19004, 14013, 53406, 5355, 6457, 2672, 42845, 22793, 21748, 9746, 42130, 29319, 2769, 22701), (27527, 62884, 37510, 21281, 10981, 4638, 34155, 41792, 63989, 1876, 27302, 18799, 44068, 11593, 50906, 40865, 49071, 12867, 24399, 14481, 19587, 28184, 48564, 45425, 7905), (55327, 30080, 30191, 48087, 39072, 14671, 58252, 3224, 30070, 52228, 11763, 34327, 4400, 35921, 42476, 38294, 19715, 55056, 61956, 37851, 7587, 35657, 9340, 37829, 54169), (51933, 6073, 53935, 12895, 55593, 12530, 44542, 61233, 60062, 22663, 42592, 10780, 14249, 50837, 38734, 33239, 15860, 31407, 29182, 43907, 14844, 38785, 24267, 26783, 64798), (55517, 20584, 17945, 53621, 64214, 2917, 5802, 59910, 53445, 37728, 55920, 59969, 58424, 35722, 55222, 15616, 35769, 34670, 20957, 34902, 17395, 37370, 10887, 23206, 49992), (37978, 58015, 16416, 14124, 47475, 27015, 38713, 18591, 34708, 42217, 62669, 58317, 64339, 25675, 17690, 41607, 29533, 24483, 55578, 57964, 41306, 56104, 55851, 48956, 8774), (22019, 27418, 54944, 50505, 19245, 20876, 14210, 18039, 28407, 11086, 6347, 17101, 35523, 35936, 39772, 40012, 8384, 36420, 54902, 21945, 6190, 177, 24802, 27178, 5492), (50519, 18630, 14295, 7962, 10410, 54499, 2849, 32734, 13750, 48281, 13649, 52739, 8010, 39736, 3683, 12160, 12087, 1093, 22075, 58169, 29209, 6529, 6478, 32426, 46547), (48083, 18917, 28158, 28322, 35740, 63287, 3077, 55031, 31895, 48070, 44569, 49778, 35721, 246, 47073, 59126, 55949, 32729, 10633, 54288, 41567, 52586, 59551, 35337, 61843), (13064, 65282, 13169, 1996, 6476, 47666, 65305, 31123, 56901, 62372, 6200, 36609, 35978, 46025, 44264, 59591, 13445, 37009, 13695, 26167, 42517, 5037, 7438, 41049, 13441), (423, 21191, 46381, 31547, 53040, 15630, 20459, 64961, 46048, 27761, 27462, 33211, 43423, 52431, 51780, 40986, 24212, 41497, 40513, 13345, 49125, 2822, 14108, 23954, 6149), (42967, 27474, 24769, 43781, 43960, 27583, 17271, 11520, 2320, 37899, 60357, 58574, 37507, 20828, 25031, 44323, 3828, 31119, 33923, 23068, 52129, 31813, 3958, 53643, 64993), (9577, 39703, 11596, 30874, 7507, 46494, 16874, 41234, 58191, 61849, 2751, 5770, 38449, 15772, 4853, 48960, 48572, 1719, 58079, 33744, 46348, 28951, 9744, 21933, 21282), (21691, 33604, 56484, 38509, 63020, 46523, 39199, 29612, 36300, 33025, 39572, 53789, 29709, 50446, 13847, 50700, 39780, 33649, 17766, 25483, 14593, 52638, 33704, 44349, 35663), (18300, 13467, 33961, 25407, 27856, 15593, 40467, 16401, 62199, 7145, 50201, 489, 46765, 35183, 31813, 37070, 45328, 17551, 24687, 9718, 49272, 12308, 46988, 48519, 29085), (23830, 44880, 31344, 36477, 63209, 55858, 19715, 23522, 40181, 31872, 57383, 21773, 19853, 52944, 26193, 24820, 17338, 28949, 25186, 41240, 45882, 15326, 53655, 25302, 55795), (22227, 48584, 64449, 29674, 64503, 32106, 10988, 36419, 24358, 56798, 19567, 42252, 1050, 10411, 12194, 4091, 8466, 46776, 1487, 54167, 34834, 45587, 35919, 24760, 56443), (25245, 57306, 63132, 31366, 18284, 63396, 36528, 29061, 20462, 7081, 58145, 24580, 44360, 13573, 38520, 25828, 5878, 14181, 9670, 30754, 33403, 35190, 60366, 27974, 22971), (13476, 35146, 59114, 48217, 11407, 61845, 22831, 27818, 44652, 46067, 52919, 3684, 25362, 37786, 13934, 1496, 13811, 51774, 56160, 37005, 35796, 18838, 52014, 58439, 48318), (42566, 36556, 48463, 35309, 27761, 57655, 42313, 15533, 2484, 21133, 32981, 58714, 24570, 28853, 44241, 27355, 12877, 18885, 29932, 8798, 35904, 32775, 32372, 15923, 21041), (35125, 8054, 24820, 17263, 23759, 14476, 62409, 51293, 47615, 40735, 58844, 61582, 38169, 57508, 36167, 32700, 9848, 21465, 3000, 42532, 32854, 57997, 45612, 57820, 54858), (10739, 29014, 43584, 12085, 13138, 63632, 21186, 46848, 33075, 54034, 22025, 63789, 50420, 7721, 57285, 43249, 17709, 61257, 23789, 37898, 44264, 4316, 49702, 7420, 60823), (16612, 54678, 54279, 49487, 29796, 57118, 14760, 54863, 39848, 46770, 27616, 34694, 30541, 42991, 50194, 7689, 23812, 15776, 33395, 65079, 9743, 26229, 47642, 14866, 57491), (30143, 22159, 42875, 11025, 23615, 9859, 17542, 41187, 47108, 57968, 29889, 44007, 49083, 55801, 9985, 13291, 11478, 51895, 27161, 53692, 46230, 38077, 50445, 11510, 7387), (8306, 18, 23880, 56789, 33292, 12622, 33678, 19680, 19628, 21100, 2032, 35934, 58561, 45446, 17218, 59857, 38896, 10691, 33386, 24910, 18911, 3873, 8607, 16424, 15006), (43793, 422, 60890, 15057, 25110, 31402, 54732, 39006, 21053, 22910, 53593, 59332, 36578, 35611, 34224, 39812, 2968, 9814, 52586, 43887, 59136, 16793, 28277, 64633, 42882), (34587, 58560, 46837, 26386, 32962, 24741, 11060, 30031, 37282, 34819, 51773, 22453, 52012, 31794, 28734, 8660, 18762, 39696, 24417, 6678, 57542, 10747, 42737, 56259, 63247), (29542, 60060, 2528, 14800, 9178, 28216, 43008, 11309, 37409, 25293, 31729, 57745, 51753, 13865, 53944, 4679, 15926, 28792, 18034, 19445, 25398, 54124, 37769, 33585, 9771), (26111, 58318, 43611, 21501, 43758, 3041, 35855, 34550, 64441, 35010, 14687, 39657, 21323, 17134, 32475, 3973, 38922, 3240, 23080, 15693, 8703, 8095, 25797, 46815, 34916), (18027, 46554, 16941, 9060, 20593, 22254, 44684, 20069, 32743, 58939, 9375, 1718, 50129, 56034, 33371, 18547, 16613, 43742, 36222, 55198, 37465, 61031, 21604, 63409, 46693), (48279, 61287, 41313, 10599, 42410, 34482, 42531, 3521, 62836, 17930, 52821, 57826, 47922, 46637, 59914, 30231, 58619, 49880, 22143, 52099, 47903, 15637, 12797, 11068, 33241), (36498, 54883, 3611, 34180, 12920, 58424, 45575, 42098, 2526, 55901, 64879, 32172, 40498, 63611, 36512, 62469, 54218, 63965, 12138, 38993, 25804, 31160, 30662, 7875, 9522), (60174, 49418, 35968, 10654, 49995, 27839, 53551, 63322, 18449, 4739, 51937, 38608, 25038, 16611, 1897, 17938, 4104, 52133, 23170, 7704, 25020, 4061, 63399, 42296, 18092), (17187, 15286, 5596, 9842, 3370, 58586, 8310, 29188, 28896, 34546, 36759, 42396, 12643, 30138, 64505, 41365, 30084, 24157, 20642, 50533, 45302, 37420, 5745, 34752, 16350), (11263, 34967, 37597, 7389, 48285, 26245, 21016, 55433, 40514, 1863, 51022, 58691, 20263, 4983, 6867, 51217, 53803, 41877, 47646, 17301, 9053, 51786, 43607, 9173, 5499), (40243, 13456, 37953, 59312, 35213, 7802, 3538, 45675, 60253, 34356, 12561, 57935, 48390, 60784, 12977, 27579, 17944, 47399, 29603, 35058, 49245, 814, 62328, 59524, 56058), (59413, 56241, 42432, 55047, 49572, 31130, 58717, 31975, 39399, 50981, 28173, 6771, 28110, 43506, 32496, 38558, 8512, 40623, 26467, 35014, 27175, 43600, 29107, 50250, 49744), (55251, 41510, 13846, 41304, 25657, 4496, 29780, 27565, 39811, 31600, 50486, 60831, 51481, 9490, 18069, 61991, 54089, 61429, 23168, 59862, 64778, 8840, 31692, 31083, 58861), (26698, 21116, 34922, 61540, 60568, 24706, 62570, 17141, 45390, 60168, 16464, 58400, 7216, 46930, 24693, 9840, 15245, 30304, 45700, 47322, 44717, 2451, 34909, 28251, 56925), (17124, 41630, 9249, 45077, 59808, 42902, 20125, 6712, 64805, 21611, 11916, 58052, 33368, 9376, 18851, 65182, 51342, 9001, 64995, 41634, 61533, 52984, 52599, 45734, 58894), (9179, 30817, 4044, 54775, 46602, 21628, 49228, 49047, 61637, 35538, 9276, 24155, 54213, 31306, 6107, 63132, 25546, 9174, 63468, 194, 20405, 7028, 13056, 43492, 56397), (17270, 5, 25946, 50928, 50994, 15162, 28510, 44769, 64877, 65081, 61375, 23405, 62531, 25229, 33310, 64358, 35269, 46830, 38236, 52803, 38843, 62649, 51120, 65135, 8365), (12200, 5770, 55023, 33456, 23859, 64550, 54633, 36962, 5572, 11250, 58121, 3037, 46744, 43918, 34459, 16159, 57401, 27866, 60569, 9556, 11394, 18150, 29026, 38961, 24158), (17131, 32806, 63894, 51616, 27370, 16552, 29915, 31781, 37746, 59186, 5254, 23488, 31754, 29687, 42381, 30135, 8319, 42920, 13186, 39381, 52983, 15047, 33962, 9249, 49485), (43024, 42920, 4630, 6000, 38644, 50367, 5416, 14331, 28429, 27344, 28142, 42350, 49229, 57146, 131, 43908, 44564, 23284, 6467, 17714, 29508, 58482, 10640, 35539, 18769), (64904, 524, 18943, 54026, 65080, 61014, 1047, 6543, 36946, 64890, 57183, 18269, 61763, 56540, 59067, 36732, 41768, 53384, 20568, 25496, 46360, 26544, 19344, 8349, 47389), (57195, 63758, 64494, 18502, 45060, 48817, 9195, 3826, 63294, 64411, 15452, 6073, 9679, 22078, 18023, 42131, 23006, 12299, 31060, 28079, 2667, 62074, 62225, 26748, 35933), (25379, 57939, 38867, 56640, 30147, 50781, 20769, 39963, 324, 62907, 37986, 13058, 41842, 21771, 9958, 15943, 15194, 59049, 11203, 46413, 63163, 12643, 35589, 38782, 35223), (4187, 3539, 33239, 50728, 10210, 4822, 21130, 50240, 40217, 47035, 44267, 54159, 34807, 17695, 58790, 45281, 21541, 40647, 35100, 10556, 54318, 54736, 5257, 18998, 47146), (26883, 36794, 44708, 55353, 32689, 45264, 3208, 51543, 60076, 22760, 40427, 57416, 62009, 65536, 24333, 11223, 10107, 57091, 14429, 14947, 61834, 23129, 1628, 55113, 54919), (41196, 10203, 60818, 25976, 42692, 20247, 51591, 52643, 24346, 40852, 55842, 47972, 24058, 47236, 17840, 7820, 47954, 4144, 24958, 49254, 18267, 35965, 50711, 49862, 52331), (41074, 48172, 34107, 20079, 30796, 55788, 57031, 35024, 13372, 60828, 9554, 56376, 56974, 31749, 55596, 33799, 27869, 60773, 43615, 24563, 17849, 4651, 43749, 53529, 4550), (5188, 27484, 55636, 21007, 37545, 51718, 16782, 32246, 36515, 44007, 43416, 11355, 15947, 43557, 18922, 23580, 7951, 63622, 56371, 26215, 22417, 33453, 51941, 47166, 23854), (64365, 15806, 15515, 53768, 12919, 35271, 61190, 46223, 36598, 24860, 27832, 49904, 34883, 6600, 30275, 51069, 43855, 43734, 28549, 41102, 18160, 16962, 18696, 65057, 24338), (57476, 37966, 58447, 17431, 44822, 16692, 53568, 49349, 39116, 17266, 54820, 28916, 49601, 45956, 37576, 18512, 12887, 12410, 25219, 35982, 61772, 31404, 61058, 26109, 43366), (14581, 27731, 47434, 50399, 22240, 54558, 2880, 32742, 45420, 15495, 39501, 59713, 62527, 57026, 24376, 26798, 25556, 36241, 48445, 62267, 65527, 11124, 2246, 51860, 14861), (42347, 45735, 61464, 30171, 29424, 61234, 32638, 29876, 9104, 65014, 5477, 45721, 29624, 4174, 30479, 13076, 54574, 39717, 9921, 27729, 12961, 12523, 26933, 50994, 13530), (35740, 27010, 35929, 7552, 33214, 16798, 54298, 41957, 59358, 42355, 41053, 37027, 50235, 32070, 917, 13466, 63683, 1485, 40881, 54845, 56655, 55439, 48579, 1184, 25122), (47526, 29793, 43119, 64547, 59549, 53721, 64139, 46604, 35810, 32616, 38399, 12220, 43927, 39471, 3224, 5410, 10810, 52811, 40784, 1295, 59055, 51529, 51840, 53467, 50303), (59306, 9403, 54790, 45782, 63263, 7291, 49836, 61967, 40079, 293, 61457, 59154, 31501, 56823, 33541, 50337, 793, 7008, 23635, 61904, 27902, 60790, 9767, 18265, 20796), (62595, 1220, 20077, 38776, 62809, 11098, 30185, 32725, 61184, 29780, 21806, 21386, 22743, 36044, 8094, 11374, 63385, 44589, 40247, 22147, 10825, 20654, 46024, 14353, 10004), (27366, 43515, 19009, 46535, 64803, 1782, 54998, 14052, 42703, 59599, 31314, 39610, 56031, 35436, 48120, 59845, 9825, 27191, 14158, 38081, 14024, 9981, 46647, 58640, 9044), (60895, 27990, 37796, 17120, 29514, 50650, 62677, 57766, 19084, 41015, 6935, 29971, 43301, 48077, 44722, 1504, 5159, 33897, 12633, 64566, 61083, 60871, 39851, 54363, 28475), (10114, 17273, 38124, 37220, 38266, 59384, 13446, 61370, 62512, 32545, 37904, 62890, 54929, 26869, 50554, 47039, 33514, 37746, 3286, 51799, 22369, 55937, 4749, 14141, 1318), (39312, 45880, 42228, 10853, 65257, 9040, 35255, 18147, 35627, 55616, 4449, 63275, 180, 35150, 32462, 57118, 46208, 57800, 27701, 41090, 17365, 14769, 33055, 26557, 26639), (50195, 34247, 36418, 41347, 31143, 58916, 25908, 23639, 29044, 43988, 20316, 49908, 53920, 56964, 63705, 22012, 49612, 49273, 21605, 6796, 13613, 17193, 55144, 38480, 22324), (9298, 63759, 43302, 34288, 15813, 14504, 54310, 47754, 56555, 65497, 16817, 7521, 48298, 12694, 57050, 51643, 28210, 48506, 49967, 19847, 35817, 61062, 64531, 51113, 11954), (43518, 21302, 58426, 64849, 8299, 3230, 39611, 30271, 45644, 65399, 24703, 6826, 22731, 28661, 20366, 53966, 35290, 25924, 32477, 43849, 5298, 52503, 42319, 1296, 41700), (50625, 5867, 41995, 52339, 32437, 53416, 29738, 61817, 47199, 1515, 24211, 24945, 21058, 56100, 38268, 17578, 32107, 34032, 59035, 59166, 45746, 18355, 60934, 18951, 64197), (63059, 46052, 3743, 50317, 17948, 5469, 46272, 13720, 17204, 41692, 63321, 7372, 64768, 23292, 27849, 22773, 42711, 44563, 59400, 50578, 44875, 53653, 43097, 7656, 35046), (32984, 3558, 28078, 31246, 48000, 27946, 45800, 2838, 9154, 62073, 50941, 28314, 55008, 45774, 22157, 19461, 21108, 2751, 25505, 4314, 62576, 50659, 3332, 13709, 24882), (11089, 48129, 2076, 57822, 57947, 43216, 55285, 13737, 37444, 9449, 9611, 49775, 15455, 11797, 45541, 3302, 33134, 4840, 20712, 48527, 19673, 7431, 18594, 23592, 42620), (16979, 33064, 18042, 62024, 6536, 7746, 56881, 63544, 40245, 65228, 10249, 25115, 50054, 30670, 4502, 46929, 1829, 50659, 39180, 2406, 48036, 33358, 7692, 26836, 3747), (62828, 30921, 43733, 1718, 33746, 5393, 38355, 58203, 21985, 55470, 58403, 61745, 62998, 40133, 38132, 5130, 51991, 35320, 41817, 11462, 11270, 32769, 51303, 20037, 46074), (47747, 649, 46390, 10909, 46370, 61118, 54735, 7791, 54576, 61155, 61628, 2810, 1646, 56671, 59303, 36601, 1844, 51204, 39865, 31197, 42895, 34455, 23747, 46672, 27047), (63976, 24868, 15777, 11304, 55868, 41172, 51128, 22202, 11365, 29619, 45443, 1741, 19381, 58844, 6023, 57944, 26863, 61104, 41145, 50122, 11642, 52229, 44876, 40031, 35052), (12311, 13872, 51675, 17033, 34645, 37542, 3113, 27980, 24138, 14526, 40808, 63301, 29445, 42041, 6303, 52467, 42514, 61615, 41268, 27284, 206, 20470, 30620, 33982, 28540), (22952, 14707, 11088, 45653, 57488, 34656, 22512, 12613, 26816, 12746, 24959, 489, 55993, 42177, 31086, 60865, 46804, 15705, 5998, 1569, 62369, 39265, 32549, 18269, 15220), (21352, 4964, 5233, 33427, 54443, 34385, 35728, 35075, 25243, 48986, 23896, 57454, 62814, 38177, 18277, 5013, 18376, 52856, 51719, 48018, 50630, 54524, 44418, 21328, 61147), (37887, 44863, 20314, 31151, 597, 44635, 9005, 9958, 22827, 15109, 65100, 40749, 49835, 64545, 36536, 52945, 7136, 61371, 3145, 60819, 40050, 48386, 21060, 62099, 28804), (39021, 45276, 58991, 57326, 55036, 48436, 23301, 8305, 41320, 59540, 64294, 49344, 16734, 12291, 29706, 50864, 38028, 61467, 51552, 6036, 33463, 45106, 6790, 3348, 37341), (25563, 19121, 32293, 32662, 37844, 17171, 59928, 58416, 10745, 12389, 53814, 16068, 48774, 50613, 43099, 46730, 14810, 65323, 43651, 52491, 44549, 43927, 56379, 13229, 1020), (31639, 54790, 47687, 45571, 64200, 5577, 48303, 9090, 65057, 36609, 13212, 32708, 29971, 18362, 38870, 63680, 43200, 10195, 775, 15024, 45388, 53380, 21660, 476, 36029), (52545, 3900, 4290, 64148, 32184, 13523, 14438, 16727, 26361, 31471, 55819, 12766, 40346, 28154, 56210, 25336, 15898, 52050, 19272, 55402, 44839, 217, 53049, 3734, 60842), (909, 48511, 8117, 1861, 18147, 37619, 46713, 42222, 33830, 55219, 31924, 4475, 52721, 2476, 27247, 27735, 42141, 18533, 31973, 32390, 48171, 51985, 17231, 39837, 43028), (14615, 19991, 59944, 1895, 52745, 3228, 60605, 12835, 38951, 24426, 2892, 12023, 37663, 21064, 4493, 19120, 24022, 46482, 20531, 47060, 18899, 58833, 2412, 55287, 6683), (47676, 60978, 62982, 12237, 52328, 10996, 22596, 27842, 51181, 11975, 31246, 61543, 53923, 27280, 5823, 21770, 16966, 57247, 26099, 50514, 8613, 51336, 35575, 55593, 52922), (62719, 48610, 4471, 13946, 36444, 1059, 43270, 7112, 65197, 61315, 20480, 42394, 42225, 14610, 56459, 27241, 29696, 42328, 36135, 33673, 533, 22872, 31157, 60619, 60187), (40961, 47625, 3034, 51494, 49977, 34070, 26517, 55509, 36765, 22284, 43282, 55581, 61725, 24244, 28637, 15899, 25524, 12599, 1890, 44716, 15770, 8103, 1914, 36226, 24436), (43257, 55858, 38007, 50007, 61659, 64256, 1521, 42787, 55461, 47913, 63753, 27450, 39779, 30760, 4849, 63014, 43042, 30005, 27127, 53489, 25960, 23085, 10214, 50430, 15790), (63810, 8194, 39100, 4450, 10501, 58064, 37244, 431, 1471, 8214, 37194, 1428, 40863, 18171, 24941, 11176, 599, 7376, 8924, 47235, 12337, 12560, 32731, 48306, 53048), (37134, 48732, 54049, 35587, 13100, 56820, 32612, 25031, 30514, 40896, 10099, 22580, 54909, 5459, 21942, 999, 3639, 26511, 55606, 57643, 48532, 38816, 7290, 59371, 63761), (43126, 12763, 41439, 17003, 32237, 65078, 63153, 62001, 63914, 22175, 64578, 10856, 28134, 27374, 39008, 47528, 14367, 8901, 39542, 48010, 274, 48297, 13433, 47332, 37045), (4250, 19383, 15695, 47339, 6670, 54355, 30210, 59626, 16614, 64609, 42389, 43557, 42301, 21366, 46469, 11337, 26063, 23435, 45045, 57224, 14790, 34907, 27220, 34733, 58793), (18702, 21535, 16899, 20248, 46872, 38013, 309, 55132, 62272, 27625, 33002, 57086, 50486, 5362, 43687, 44157, 54518, 56305, 20938, 15498, 12572, 54012, 49570, 1121, 31594), (10674, 61967, 30725, 46727, 31556, 19730, 60681, 4387, 65238, 32940, 39165, 25698, 36756, 44546, 62933, 39947, 64032, 27034, 4811, 374, 15867, 28913, 29586, 36541, 30563), (26403, 48639, 43268, 826, 15399, 185, 61849, 53072, 12465, 33347, 48224, 7581, 29516, 24443, 3224, 32145, 4076, 4962, 57916, 63202, 23154, 28326, 43148, 43891, 8327), (9824, 59988, 8699, 44252, 21984, 49600, 17461, 41457, 7579, 44208, 62468, 4393, 20787, 8917, 15674, 47498, 35297, 52753, 28011, 44873, 9803, 23879, 5658, 44282, 46427), (47062, 42967, 57150, 25004, 51237, 65498, 47032, 51249, 26974, 32216, 790, 33592, 47455, 51069, 53988, 55738, 41098, 35272, 11276, 9698, 18666, 26787, 18601, 19967, 15997), (59308, 25393, 54561, 18206, 9617, 15946, 41316, 53014, 13237, 64087, 14075, 24323, 42592, 3233, 21980, 40693, 48062, 4717, 43004, 6265, 62019, 47093, 46018, 23482, 35175), (58753, 57305, 62731, 18802, 62583, 5185, 14875, 49398, 42171, 31482, 29019, 30657, 27379, 10016, 43507, 39770, 58297, 62829, 37302, 53881, 55720, 46626, 57795, 42980, 31241), (58901, 23103, 37456, 18301, 61411, 10580, 15377, 62307, 34526, 51735, 22582, 32560, 41562, 2059, 58443, 40532, 23839, 28598, 60449, 52914, 3396, 60453, 12879, 31387, 45879), (40345, 22651, 7994, 38498, 55254, 62841, 47170, 34514, 3009, 14979, 17475, 7526, 19499, 50783, 15991, 14168, 3453, 58310, 40106, 10045, 10636, 17001, 63246, 63855, 18861), (60659, 14422, 15515, 52224, 4270, 55942, 62587, 27058, 57328, 27406, 147, 21506, 16329, 49090, 6696, 42398, 22823, 14350, 38446, 35681, 13302, 64952, 45361, 26491, 51962), (64479, 30943, 4601, 14316, 18992, 65516, 55528, 37439, 21522, 5819, 17342, 20188, 61318, 32426, 27200, 19511, 49448, 9772, 32800, 65275, 13040, 17349, 2444, 6439, 36753), (34910, 25125, 29495, 34917, 48473, 62897, 47536, 29098, 29574, 44535, 24170, 59716, 23430, 18679, 27716, 63167, 8063, 4815, 55980, 1622, 55095, 45109, 1949, 5896, 60986), (61283, 2452, 39849, 13690, 26027, 39269, 57930, 8698, 16084, 16317, 41970, 56054, 1382, 27280, 26952, 49504, 23990, 10871, 37697, 40664, 52741, 21053, 7048, 31233, 56112), (26674, 32686, 1212, 31269, 39950, 39872, 29258, 7137, 51689, 13017, 64840, 3535, 50386, 13821, 21446, 21950, 61470, 27931, 47173, 22380, 46020, 4117, 15396, 59489, 2909), (55132, 51696, 43642, 34242, 44705, 16232, 60807, 26198, 3531, 31060, 5176, 7584, 53308, 35064, 44459, 27714, 3543, 50992, 39850, 61148, 35488, 45389, 54721, 47403, 15739), (39097, 14986, 7883, 61660, 29132, 9251, 12910, 58870, 29699, 32537, 38785, 14130, 24262, 41001, 35280, 2299, 62964, 6242, 55386, 25771, 50803, 23110, 45857, 56902, 20881), (8631, 45335, 6279, 32475, 25502, 7450, 62555, 22256, 2296, 60254, 45090, 58378, 58647, 36081, 64576, 59119, 16226, 15852, 38831, 44235, 56781, 41709, 11666, 51599, 32087), (44623, 54569, 27776, 1603, 7047, 57895, 23725, 34461, 41437, 32036, 24868, 63680, 24673, 49825, 56022, 18618, 17320, 6607, 41885, 31794, 16650, 48196, 37166, 61959, 56712), (39103, 18449, 14006, 26745, 348, 50946, 6724, 18981, 23055, 63308, 30741, 18070, 39912, 32625, 28731, 52921, 44820, 13776, 46540, 47024, 52892, 21674, 45459, 50547, 2672), (23779, 41364, 14549, 11537, 24837, 36131, 43939, 12562, 448, 37493, 8432, 18984, 35808, 33830, 48391, 46120, 40784, 4393, 44286, 38432, 35139, 6417, 61812, 18666, 47888), (29423, 59876, 46450, 60950, 30243, 41672, 571, 26630, 24227, 63051, 5757, 41999, 54048, 52982, 55138, 25262, 57207, 62183, 4013, 12307, 12908, 50075, 36174, 25283, 56749), (39565, 56106, 23712, 60001, 29255, 35484, 51670, 54630, 54578, 32208, 60200, 45590, 34141, 8191, 55863, 5070, 41527, 5241, 25445, 54154, 41762, 38628, 17597, 7833, 37713), (2172, 3183, 56140, 65135, 58780, 30276, 24649, 34649, 63123, 30296, 5303, 29313, 56097, 62537, 39319, 42667, 1233, 13113, 22653, 21396, 32224, 64459, 51237, 29929, 50744), (63971, 26988, 62122, 40979, 27083, 13102, 9272, 11839, 59655, 50304, 39642, 28989, 22958, 16997, 55006, 65198, 61843, 26535, 23269, 41535, 29410, 34057, 34456, 47372, 32093), (36567, 9259, 53914, 57268, 32128, 54378, 949, 39784, 44438, 56657, 5619, 30363, 56016, 22038, 16671, 62689, 50148, 10726, 61655, 26355, 14354, 29300, 34201, 2496, 54713), (51870, 18307, 25344, 62217, 45181, 63744, 9978, 30098, 28165, 60759, 38466, 23596, 36121, 38305, 26709, 51704, 46279, 28053, 44686, 26032, 25275, 37080, 55503, 5899, 51575), (45819, 62884, 50155, 35625, 33683, 36297, 33367, 43974, 52809, 51616, 64166, 44504, 65379, 64590, 53970, 48115, 10737, 50633, 29595, 528, 1387, 64882, 63595, 24073, 51950), (23392, 30925, 63565, 29319, 45708, 52981, 18077, 21812, 480, 32365, 54601, 28450, 3872, 23443, 19478, 40030, 40813, 55457, 35010, 31477, 61179, 20918, 10736, 57885, 50340), (55622, 40790, 63601, 39127, 13665, 44781, 36092, 5240, 10683, 37153, 1305, 55636, 26638, 13985, 17009, 42313, 55293, 34721, 62646, 54308, 37736, 18180, 12730, 55532, 2110), (34684, 16106, 10537, 5684, 49681, 38220, 50159, 63284, 54313, 34714, 39890, 46718, 53879, 55770, 22899, 26895, 12509, 54472, 52978, 25961, 62700, 52084, 2081, 32252, 54600), (46555, 58835, 221, 19911, 30555, 30983, 32124, 42596, 17553, 24848, 8917, 41457, 35408, 5516, 10669, 9528, 59100, 4427, 5840, 35807, 20687, 11036, 25846, 33594, 31058), (28961, 32788, 59796, 32220, 34559, 53797, 47008, 60589, 47961, 54871, 20330, 38828, 20102, 33637, 43509, 47371, 22288, 33102, 58982, 11734, 1844, 57427, 14513, 1055, 31274), (31577, 16645, 37450, 27530, 45821, 55915, 64062, 29893, 41860, 11473, 41054, 58639, 27557, 18523, 7943, 5704, 61155, 63570, 31665, 52775, 57601, 5624, 29517, 46607, 2288), (46251, 62079, 31611, 33088, 61650, 9166, 61974, 17027, 5101, 38831, 46704, 37671, 32677, 33613, 65497, 35430, 30159, 61612, 53626, 56918, 59183, 11419, 54778, 22895, 16399), (58372, 6278, 15350, 50003, 6403, 44041, 27918, 32026, 44446, 48912, 46667, 39664, 15144, 56228, 6252, 20761, 52713, 17082, 48032, 17414, 15465, 65155, 51914, 38536, 17192), (5612, 13381, 59113, 25154, 24528, 818, 65199, 61092, 23613, 6713, 56937, 19345, 31009, 17505, 48012, 60353, 37459, 51591, 9697, 22700, 6810, 28368, 62507, 11242, 61150), (10660, 60920, 22980, 35924, 4261, 50190, 34911, 33724, 18483, 4546, 57989, 58970, 30532, 64358, 7904, 31792, 30209, 56783, 9896, 37252, 25307, 14192, 30955, 22530, 16901), (19507, 27987, 32086, 23004, 23157, 31652, 48117, 36622, 61371, 37374, 23273, 51879, 25662, 23991, 4004, 30537, 58629, 32279, 51698, 30272, 14069, 42209, 22324, 11061, 63242), (3106, 27200, 23282, 21885, 33153, 61937, 45662, 55607, 22047, 29251, 17789, 3519, 25825, 54858, 30742, 57991, 47770, 58677, 39274, 47963, 59334, 37958, 31012, 63474, 37864), (44963, 40479, 16917, 36471, 37284, 37812, 59772, 57281, 515, 40090, 26652, 9411, 52778, 60856, 22764, 34341, 21189, 61880, 5887, 1663, 61009, 62411, 34785, 50597, 3001), (5123, 50044, 62338, 21726, 39000, 39349, 38980, 11343, 50982, 15155, 6750, 52925, 11633, 2342, 50508, 46964, 63975, 591, 26595, 41183, 19167, 15590, 23552, 24658, 7398), (34449, 46181, 24676, 58914, 27267, 26071, 59236, 59005, 32575, 65430, 22601, 29579, 63313, 26340, 25200, 7190, 15873, 64493, 56548, 47646, 46627, 33634, 46744, 54882, 15043), (12150, 15304, 32548, 19841, 24850, 49499, 59436, 25969, 53866, 22824, 52799, 45085, 62576, 11497, 44601, 48436, 43235, 4755, 40176, 17918, 20271, 25802, 23723, 47457, 32736), (45123, 58964, 41639, 58005, 32551, 1793, 27764, 30696, 61088, 33853, 446, 44007, 63743, 48723, 34828, 54006, 23573, 24623, 10126, 11598, 42728, 41642, 826, 34185, 65530), (52540, 63073, 4837, 45273, 38472, 56611, 34606, 28445, 14680, 44812, 22445, 58004, 61320, 60405, 58276, 20488, 18702, 63052, 3116, 7091, 17219, 31793, 6534, 62066, 15075), (4880, 7115, 56456, 49194, 3177, 8353, 61296, 29169, 18153, 2260, 41957, 28041, 423, 21530, 61436, 29168, 37569, 39065, 30265, 24187, 910, 9973, 43874, 37940, 29283), (27151, 57333, 4199, 60468, 38257, 24346, 29085, 10203, 64008, 20158, 51380, 60687, 11472, 15266, 31680, 16898, 15340, 48415, 59249, 42429, 11336, 32272, 38669, 61347, 11186), (215, 52961, 54735, 62705, 62111, 27796, 19127, 22933, 50099, 9407, 31310, 59074, 47309, 54576, 25961, 22105, 1770, 54380, 58240, 2788, 14728, 22821, 9517, 65325, 41139), (51041, 62817, 52065, 26515, 45088, 52009, 6982, 23671, 27094, 28562, 40182, 50407, 62645, 35450, 43916, 61966, 40381, 1627, 51722, 35171, 56486, 39222, 65058, 31435, 28493), (660, 63661, 42221, 23, 18759, 29256, 41353, 60185, 56449, 60830, 8498, 6411, 60718, 42948, 59185, 18158, 47104, 17810, 61599, 45674, 61394, 44693, 43405, 4421, 663), (33764, 45310, 30003, 41283, 7531, 34882, 47448, 27643, 45765, 61679, 29546, 21504, 23424, 14722, 52571, 46567, 10598, 56891, 24939, 13403, 37688, 20133, 39768, 19705, 33269), (20093, 55118, 11078, 15599, 25680, 18198, 123, 38062, 4148, 52210, 7815, 13641, 2229, 261, 4416, 40529, 55183, 7326, 16651, 10873, 54467, 35190, 2266, 11266, 29929), (26737, 29329, 29596, 32042, 12530, 56810, 47687, 41512, 46545, 21225, 13250, 44012, 22857, 59911, 29331, 5686, 60557, 34521, 22112, 55483, 15383, 8288, 27821, 38448, 21396), (61481, 46113, 33447, 53780, 13613, 16890, 45396, 22748, 45606, 26133, 35988, 47718, 64437, 22416, 5984, 1934, 23481, 34830, 42766, 26658, 31473, 40711, 29347, 22341, 52413), (26019, 40310, 18971, 5416, 1250, 33392, 65090, 10478, 56075, 45048, 13943, 37596, 2392, 47398, 744, 41113, 48158, 11494, 18107, 61881, 15691, 57624, 43719, 43841, 42080), (3145, 39915, 50901, 48035, 55315, 36734, 1201, 16024, 48784, 18286, 7139, 11042, 2524, 11514, 60810, 39294, 37896, 41003, 32627, 28360, 50035, 13318, 26907, 22586, 31125), (36845, 4208, 19450, 20874, 38539, 18097, 16110, 61320, 47555, 4545, 34881, 27567, 18818, 14466, 27977, 29311, 23689, 42846, 11196, 34847, 43056, 28899, 24103, 417, 3477), (40806, 63390, 24480, 47249, 26895, 35083, 48434, 39951, 45873, 16198, 5518, 23551, 50258, 59534, 32745, 43479, 5479, 15038, 42727, 65211, 29659, 799, 55715, 4225, 57678), (19156, 6356, 42091, 28803, 22571, 6748, 59917, 51029, 64698, 46231, 45685, 6906, 58663, 31318, 34777, 82, 21916, 11769, 49161, 63293, 53420, 17641, 56675, 48228, 19496), (47404, 28030, 19852, 46667, 16928, 11422, 62434, 31940, 39707, 51037, 20898, 37944, 39802, 50655, 42138, 41450, 1819, 31052, 47560, 23860, 11820, 62187, 19128, 36648, 57573), (54897, 21448, 55804, 16368, 26837, 36501, 1333, 33454, 26101, 62898, 53562, 8202, 59154, 4467, 8230, 2829, 9641, 21418, 12025, 3525, 28548, 28061, 44734, 18060, 51634), (17007, 37500, 65253, 58547, 52355, 14898, 318, 46677, 49360, 53252, 10293, 15568, 33867, 65158, 6398, 32644, 13795, 58906, 51899, 25865, 27782, 8896, 28653, 24571, 18257), (4695, 61950, 39989, 44970, 54059, 23739, 44633, 35606, 34872, 22663, 24597, 36054, 33672, 41739, 6319, 2631, 14160, 43107, 46118, 47704, 61807, 63074, 11663, 46149, 10001), (17704, 59655, 6139, 39229, 4201, 17078, 18282, 10617, 8382, 10433, 986, 51102, 33772, 20782, 14220, 41020, 12900, 11425, 58242, 13130, 63462, 33595, 16952, 63610, 27359), (39468, 10250, 22224, 58034, 5571, 38027, 13992, 3800, 61456, 55607, 12469, 30158, 1208, 37856, 8040, 47772, 20908, 2385, 22740, 54040, 4951, 9145, 16251, 33328, 18895), (24072, 22921, 51081, 48555, 65285, 288, 39323, 26084, 58413, 57715, 50007, 21627, 12541, 2917, 53983, 45811, 15993, 26505, 29335, 13595, 54881, 44877, 7288, 7589, 65039), (4237, 61018, 16408, 52329, 30446, 17430, 49509, 46665, 13676, 57665, 38199, 21608, 55377, 11165, 36945, 5986, 25665, 63653, 2174, 15105, 39765, 28050, 39036, 37682, 9663), (19736, 32842, 7802, 9801, 18085, 36065, 33846, 36499, 1714, 13764, 22482, 60122, 27665, 12684, 34793, 3615, 27992, 1202, 44757, 35174, 19915, 57496, 24505, 55481, 29454), (14964, 52068, 10246, 21070, 12665, 21399, 24461, 25519, 1686, 61727, 52200, 39969, 4069, 1400, 49038, 9730, 42029, 18642, 7163, 5397, 6437, 51660, 40312, 2491, 13783), (42978, 967, 2070, 13552, 53040, 44222, 14173, 59752, 11199, 26779, 39798, 45774, 23358, 46901, 26583, 4239, 36446, 43829, 21607, 5806, 16799, 5951, 22606, 3342, 36551), (43772, 2157, 50874, 35990, 18910, 31321, 46227, 34378, 19435, 63003, 35057, 10279, 35486, 46177, 41012, 10803, 39848, 2902, 8722, 14212, 18325, 28969, 3481, 54528, 10498), (34777, 26941, 47421, 46380, 36674, 1203, 20714, 57854, 39875, 12223, 31615, 4366, 48417, 11911, 36400, 55238, 35099, 36801, 57740, 61607, 9321, 3177, 26536, 38898, 29786), (26138, 38130, 53, 32293, 23976, 11968, 32466, 18079, 9800, 43526, 58994, 41052, 15752, 49129, 4959, 19094, 18585, 6939, 37999, 64480, 43000, 12113, 5651, 7113, 54921), (1449, 47370, 60675, 7731, 4437, 16191, 54378, 30403, 57329, 33571, 5660, 51439, 21437, 46182, 32787, 33260, 38567, 56753, 43212, 49048, 14576, 18973, 15810, 23847, 59163), (25137, 62313, 50420, 11728, 50133, 26754, 8635, 416, 44633, 23890, 48741, 62155, 8946, 39241, 24470, 59434, 21249, 23744, 16483, 44771, 42412, 61183, 16309, 59233, 61568), (37014, 35736, 13422, 16622, 43872, 48255, 10373, 33179, 32460, 23470, 23633, 42333, 26754, 21496, 1710, 15194, 9548, 3212, 17331, 11662, 51001, 52606, 63025, 30479, 20386), (11993, 32632, 1079, 37037, 46565, 17320, 18807, 22759, 50412, 22524, 22966, 28050, 59996, 19225, 36977, 37646, 55152, 10589, 49742, 22305, 45001, 3969, 6222, 9627, 51969), (6434, 37643, 35889, 15859, 7718, 5250, 23220, 40860, 45047, 36650, 56474, 5258, 46209, 43550, 46571, 11101, 1984, 36156, 55141, 59154, 14570, 65495, 58500, 25748, 48845), (35544, 1147, 54943, 58764, 6970, 15728, 11845, 11800, 22887, 47359, 64179, 31951, 10323, 64171, 53169, 20096, 20909, 60223, 2248, 10496, 13822, 29106, 35926, 5892, 53392), (64023, 16235, 20702, 709, 39469, 22065, 50421, 62408, 46605, 16353, 370, 6550, 56607, 61568, 63766, 19701, 19963, 56410, 58695, 42276, 61998, 3313, 27602, 35136, 13165), (2940, 52533, 60112, 37695, 53776, 7382, 30514, 28259, 42965, 41336, 21072, 53706, 58455, 37276, 33611, 833, 55537, 7241, 64371, 13204, 4736, 10234, 43032, 15132, 18007), (59329, 11759, 42233, 33594, 20400, 54472, 58356, 45076, 24685, 21909, 21023, 31814, 4702, 16259, 58802, 18911, 32775, 12966, 41586, 50158, 26766, 63682, 43585, 12018, 20245), (16244, 23599, 30005, 31779, 6481, 38810, 12950, 10407, 20544, 52384, 29259, 36599, 64898, 8413, 50200, 49072, 30891, 54123, 38399, 12018, 61010, 3412, 42941, 5419, 38746), (64640, 55216, 17734, 58021, 42301, 48293, 60315, 57111, 15332, 7761, 5839, 37829, 23465, 18592, 27214, 23132, 45678, 63827, 28812, 19300, 21915, 29096, 34914, 3712, 14236), (14314, 46645, 6408, 62129, 60528, 35373, 58543, 9085, 30585, 51774, 26448, 10434, 20544, 22099, 25380, 60479, 44540, 8193, 18148, 7244, 62958, 53217, 63966, 20427, 27312), (9763, 65027, 8290, 62557, 28468, 48098, 34584, 19003, 17260, 26997, 60760, 27641, 24301, 30208, 62229, 64905, 36834, 42925, 33319, 4919, 62278, 22794, 59389, 15796, 13601), (38904, 27063, 47554, 44601, 50322, 12079, 33598, 55352, 43863, 41732, 30632, 8350, 56475, 34937, 60682, 30434, 19671, 38721, 29335, 25343, 36914, 15986, 47921, 19073, 29371), (15792, 24716, 54884, 33540, 33515, 8746, 43195, 57997, 40653, 33652, 25610, 8213, 16233, 33126, 33771, 38206, 35464, 12916, 48506, 7888, 53722, 47819, 57071, 62311, 12187), (59100, 60809, 12646, 64493, 1254, 37133, 53839, 44824, 29749, 31781, 3292, 1317, 56456, 43314, 19712, 45563, 17077, 14522, 24656, 694, 18746, 52845, 17178, 29090, 50596), (19240, 47684, 23573, 14298, 970, 16468, 10897, 15703, 2334, 52501, 64468, 40540, 5432, 40011, 12454, 56168, 34054, 64649, 4698, 29365, 53679, 21009, 20082, 62156, 50291), (60202, 29395, 15459, 56724, 31338, 20230, 11210, 35572, 46571, 40067, 16269, 48224, 10634, 2958, 62914, 32502, 21168, 26838, 30149, 12148, 33153, 44383, 64883, 22412, 65465), (23774, 17002, 6082, 42936, 14460, 19118, 47085, 62171, 29970, 4119, 14835, 51283, 10195, 35018, 2834, 36921, 57234, 23818, 17909, 45004, 49723, 7976, 25988, 37511, 29667), (24261, 24015, 52245, 26529, 12432, 57407, 15228, 33235, 44573, 5337, 16263, 31377, 49607, 33321, 10209, 19084, 24743, 45201, 54215, 54066, 13103, 63602, 37000, 2297, 51144), (43658, 15380, 847, 15048, 41366, 35652, 50125, 33609, 47997, 16078, 15246, 47573, 61151, 10266, 35410, 47879, 2054, 9200, 9482, 53958, 12286, 19450, 50466, 553, 63493), (48261, 49712, 33275, 34870, 51997, 62833, 31164, 2270, 64648, 8931, 52963, 41542, 5682, 2618, 11968, 1839, 14144, 1339, 33752, 26840, 10107, 15526, 60842, 43713, 47195), (13861, 57966, 9728, 21495, 51231, 4314, 48674, 42384, 56981, 26718, 35201, 47016, 10038, 22504, 18556, 21560, 1691, 10876, 43190, 60762, 46554, 57421, 41538, 26489, 27062), (43620, 44751, 29179, 1776, 11195, 4579, 32208, 42425, 25055, 46041, 52576, 19310, 16035, 37681, 27872, 55640, 54019, 44771, 4001, 44431, 61402, 36612, 41353, 40292, 29186), (28618, 55946, 53668, 34859, 15126, 55776, 21618, 27107, 57685, 37920, 35077, 8075, 32572, 23570, 65126, 22258, 50767, 24243, 57060, 9587, 45285, 982, 54980, 782, 57156), (13551, 59022, 16773, 53150, 35696, 46755, 634, 53786, 2090, 14867, 50390, 9952, 20055, 64829, 55477, 42483, 32200, 9728, 49643, 24634, 57884, 48925, 1616, 50258, 30899), (53266, 59512, 50251, 65012, 38884, 20782, 37426, 8155, 2769, 10439, 48371, 30174, 10228, 51562, 7323, 28349, 49315, 52374, 46346, 50802, 30339, 51922, 7640, 56817, 22254), (17297, 31720, 11421, 40806, 39205, 16343, 17562, 44849, 13263, 57447, 24724, 29440, 31191, 55769, 45813, 57030, 29151, 55833, 49240, 50484, 55093, 55028, 40833, 62138, 42079), (54058, 31923, 63533, 65254, 23, 12511, 39914, 19413, 24382, 43322, 43796, 63902, 63566, 59017, 41256, 23559, 13428, 30143, 10011, 44624, 40190, 25184, 1409, 38644, 17967), (1753, 26025, 16841, 24880, 53487, 14120, 60974, 32531, 18832, 39533, 1666, 6964, 5496, 2906, 54709, 45434, 16306, 7747, 61826, 37238, 48060, 36910, 35009, 2686, 30230), (23452, 40578, 5854, 57163, 43004, 14965, 63754, 5051, 6371, 19831, 57571, 152, 44252, 671, 17313, 40616, 63055, 33720, 21121, 41171, 3219, 14592, 47213, 58047, 60790), (51805, 19597, 43254, 10323, 18339, 19612, 65389, 48364, 29954, 48542, 64305, 65220, 56755, 26145, 62412, 62517, 39454, 671, 13041, 19522, 53535, 33295, 26260, 10918, 44317), (38338, 56041, 53702, 64423, 45803, 50120, 52285, 13489, 27169, 5102, 62237, 4859, 39380, 22855, 19058, 46799, 31246, 37570, 13063, 44310, 16944, 9937, 9567, 49624, 22496), (43186, 44951, 38937, 55448, 1556, 60862, 7850, 18072, 28904, 37186, 15942, 2575, 13902, 36913, 28979, 55647, 43182, 22426, 42775, 12443, 14071, 42959, 53728, 29510, 25484), (17441, 43859, 35384, 2214, 58195, 30757, 63089, 58613, 42919, 55021, 3747, 16982, 30375, 35179, 32861, 31095, 12898, 56057, 1578, 58553, 58278, 531, 24623, 20598, 59308), (1918, 38063, 57302, 6551, 27800, 59030, 19220, 35633, 25238, 40599, 24616, 3946, 49092, 53921, 37857, 30372, 10626, 29422, 59458, 29957, 7127, 62570, 48495, 16876, 5851), (18273, 21164, 46695, 47829, 10834, 46410, 3584, 59315, 16910, 21340, 44975, 45488, 54244, 8329, 7292, 39577, 46324, 16320, 24721, 46242, 57997, 30485, 33416, 19268, 59499), (60449, 423, 4459, 33337, 41956, 57224, 21728, 48854, 57465, 53481, 8929, 50555, 37278, 27092, 62853, 50882, 1618, 25025, 52980, 6810, 31946, 16015, 33286, 56368, 30589), (26446, 20953, 29959, 9395, 13406, 29613, 13623, 46387, 50721, 27830, 38015, 58423, 39055, 28302, 65436, 3306, 18883, 17076, 22882, 34320, 63431, 12469, 31662, 23185, 17948), (1036, 37869, 13644, 26493, 23623, 52986, 21419, 24327, 31787, 54900, 30245, 42914, 19177, 63890, 31785, 30818, 21710, 14365, 61369, 25041, 24812, 46644, 14526, 33609, 63797), (15059, 21563, 43887, 47026, 29989, 58695, 37128, 49282, 8346, 21840, 30072, 7636, 35585, 56218, 27164, 52883, 48608, 53617, 57323, 40099, 18885, 3406, 18206, 54195, 42856), (6991, 39604, 28525, 37391, 60244, 20879, 20826, 51826, 30553, 60353, 58631, 31149, 23647, 18948, 39411, 15362, 43179, 43171, 58921, 37873, 32404, 29367, 44427, 55565, 146), (51145, 20462, 25381, 63086, 38214, 306, 25571, 52189, 27133, 24706, 47497, 64928, 8691, 12830, 14212, 40774, 50051, 36901, 15975, 17474, 34947, 25766, 740, 37631, 5604), (16167, 59916, 7450, 8041, 19074, 20980, 32311, 55496, 45295, 37573, 39533, 37346, 57033, 34026, 8362, 36567, 6062, 22483, 27006, 38472, 55476, 41701, 60640, 37999, 31030), (830, 31003, 36813, 24164, 35576, 35917, 23457, 12754, 13100, 22337, 35936, 46388, 17065, 5292, 21721, 64985, 10281, 13088, 1294, 62090, 39086, 36294, 49775, 53269, 24581), (31223, 288, 48267, 26351, 17907, 61654, 22323, 32790, 7019, 39015, 45943, 15605, 23097, 10312, 2846, 6619, 13143, 63939, 38705, 12870, 12573, 31433, 17258, 28900, 302), (39710, 2492, 64742, 21993, 31427, 38101, 7854, 37906, 41331, 63489, 60275, 5465, 19905, 32533, 63320, 11536, 33884, 64369, 32178, 65276, 38160, 26542, 23212, 13263, 34842), (22993, 28281, 26429, 6310, 60248, 784, 29722, 23965, 39383, 58948, 6379, 21935, 12817, 51542, 58567, 46467, 24132, 50754, 25057, 14323, 44589, 14475, 33398, 32318, 30905), (57649, 46126, 56519, 53383, 63977, 47993, 48613, 16622, 56893, 38824, 46609, 6547, 34910, 19837, 26129, 43479, 16148, 33446, 11773, 25231, 10129, 9406, 46016, 16573, 55987), (20845, 5671, 24459, 31037, 27131, 40074, 49130, 54831, 51414, 23543, 30613, 50119, 717, 2713, 17786, 15859, 31815, 35878, 11808, 55485, 29975, 6591, 48048, 52947, 25526), (46660, 44657, 2352, 40907, 3318, 3565, 34956, 49067, 61029, 27319, 48113, 1741, 5498, 20496, 40666, 26037, 2379, 65154, 7730, 28447, 42683, 56679, 39399, 6941, 64136), (50326, 57049, 5750, 18480, 34432, 64185, 40687, 41542, 49567, 51147, 59933, 2559, 28292, 26308, 8923, 16699, 48589, 10906, 13590, 26004, 10459, 59913, 36638, 3864, 25633), (37440, 13670, 37232, 44378, 56752, 31411, 7964, 31126, 40701, 13399, 10436, 51543, 37800, 47577, 24319, 40208, 24431, 18733, 25790, 36267, 11300, 44462, 50847, 33264, 27489), (16576, 25659, 6628, 13021, 45330, 23044, 46715, 44261, 49135, 11531, 52710, 64240, 10276, 18330, 47385, 33371, 39305, 51744, 41362, 62947, 62533, 12257, 8024, 39083, 16320), (13916, 57012, 6731, 3892, 13366, 2636, 28438, 29022, 56150, 43500, 2826, 13158, 25287, 26303, 27439, 30036, 49083, 56041, 52696, 48083, 4178, 27546, 53077, 29681, 48923), (61562, 36381, 18757, 25337, 64271, 63139, 19665, 1066, 56098, 14936, 52000, 26398, 21552, 23428, 8447, 36200, 65019, 29449, 25090, 3775, 34394, 64921, 26532, 33830, 54021), (10098, 24300, 45155, 47525, 691, 48431, 34658, 31982, 60096, 59486, 55328, 36187, 16005, 9737, 24974, 19434, 28088, 43907, 53092, 15345, 55318, 51628, 15167, 64864, 7331), (13415, 32505, 61911, 27080, 18194, 37618, 50016, 51023, 57108, 39362, 13248, 32899, 4827, 19485, 29663, 20071, 33175, 43727, 4279, 62120, 60006, 33920, 57749, 8943, 59076), (54157, 62454, 64453, 35718, 52045, 38484, 18923, 61517, 10049, 31748, 10422, 44049, 30769, 9828, 47055, 50938, 44920, 5087, 4819, 48856, 31334, 25178, 12105, 41493, 41428), (62091, 684, 46909, 60760, 15745, 29567, 13223, 16214, 31009, 34727, 17438, 62137, 58723, 37755, 64017, 7756, 35552, 31622, 50790, 28245, 54391, 19748, 5457, 39002, 15928), (43272, 49074, 10483, 56836, 15918, 37245, 3050, 18273, 23373, 33753, 26467, 12117, 29561, 56880, 55384, 57074, 27533, 1591, 41429, 42954, 5934, 30476, 41292, 39781, 59670), (45791, 29102, 42880, 52538, 38135, 32815, 45652, 402, 12230, 21126, 15909, 28290, 27602, 11895, 24114, 15827, 5825, 26456, 4476, 24474, 62117, 31684, 35409, 14581, 17987), (7427, 14486, 10498, 39512, 64977, 38283, 25140, 62270, 46827, 21569, 10663, 19124, 55452, 37505, 28174, 50063, 36858, 53646, 41460, 3910, 21464, 5880, 49375, 17627, 34027), (47667, 28229, 23089, 61518, 32114, 32720, 43194, 29789, 19735, 31021, 31538, 17395, 62672, 52193, 42728, 48416, 30905, 39693, 26887, 30352, 18803, 42691, 63436, 33099, 23741), (39327, 14374, 4187, 43218, 18853, 23606, 46597, 58489, 10663, 6351, 9898, 20636, 2474, 57482, 41004, 25662, 7430, 40614, 56417, 46514, 50582, 25448, 12974, 6806, 17121), (28383, 17949, 38936, 18797, 64953, 28907, 35457, 33803, 40574, 19463, 32168, 50311, 65242, 2799, 23589, 42435, 57204, 47114, 11517, 22307, 12373, 29322, 5328, 20887, 64341), (8316, 64844, 41386, 5044, 61653, 39035, 32908, 26227, 49658, 27670, 42043, 7679, 40197, 4648, 29999, 14832, 58553, 6523, 54270, 63462, 7673, 40345, 43050, 43293, 55299), (6931, 28079, 33293, 42295, 54251, 6868, 34025, 49204, 56964, 62568, 21373, 51802, 45493, 53095, 8540, 257, 15964, 8180, 11519, 6004, 45930, 26401, 57078, 16707, 57387), (61435, 22625, 13931, 34903, 15259, 4346, 58541, 19458, 43857, 12895, 47766, 57556, 7926, 47354, 13255, 33849, 25989, 4652, 37477, 24217, 28706, 14429, 33739, 43017, 43110), (58903, 41394, 49043, 15362, 42950, 25938, 41200, 55442, 35004, 58329, 20621, 39498, 61708, 6570, 9871, 23809, 26960, 11168, 34077, 41187, 64996, 48347, 64206, 15350, 54167), (56435, 7507, 51734, 19631, 45718, 8338, 60722, 24130, 47544, 4544, 18210, 42999, 58706, 30450, 48805, 15340, 24595, 40740, 8985, 39640, 607, 15130, 54973, 59275, 12652), (3809, 32789, 36893, 65439, 22530, 33860, 59931, 31185, 43402, 8303, 57501, 41478, 1849, 20248, 34227, 36139, 35201, 43966, 30078, 28484, 23725, 21442, 31102, 27671, 48475), (49638, 59410, 61719, 26196, 17434, 13641, 25184, 47999, 19402, 21550, 18418, 63150, 23117, 31106, 1081, 47326, 19001, 15456, 60388, 39358, 31667, 32111, 12214, 2455, 57416), (53104, 18057, 16450, 10305, 42515, 16468, 27868, 35732, 6230, 37315, 56659, 34082, 19519, 38998, 34618, 53585, 62757, 6038, 62619, 39618, 44774, 55855, 56626, 55362, 37961), (51787, 5990, 3942, 38551, 44484, 7248, 28127, 21851, 62404, 38850, 55312, 1776, 64507, 38630, 36025, 8693, 20082, 26603, 12194, 36985, 26668, 30900, 19469, 48547, 18250), (15089, 45107, 28350, 50635, 56215, 6967, 17262, 13868, 36959, 42293, 51989, 41518, 26284, 38157, 34658, 49469, 53093, 42058, 15513, 8792, 7828, 48153, 59607, 38057, 2838), (10992, 44898, 37297, 22464, 2759, 34119, 46021, 43919, 41927, 50678, 43262, 52061, 46845, 36943, 13243, 40441, 17383, 28732, 18684, 22544, 19633, 2010, 26330, 56359, 32738), (28604, 13581, 57728, 12925, 12628, 36920, 43952, 49158, 54204, 45668, 54969, 37016, 25142, 52568, 7080, 24925, 64183, 63742, 20332, 20222, 1470, 46426, 59951, 61914, 7829), (57692, 17812, 22921, 46108, 20796, 54611, 61716, 15353, 12253, 28407, 26716, 29657, 36097, 33953, 6137, 61471, 38789, 50739, 6914, 20905, 14195, 47679, 8591, 4434, 34587), (36397, 18482, 4789, 13429, 39519, 34926, 6460, 25408, 31359, 45028, 28675, 22900, 58655, 43687, 28285, 18048, 34921, 29010, 26615, 62016, 130, 40190, 36149, 50116, 56779), (42080, 38452, 26210, 35192, 25817, 41205, 18050, 25846, 3113, 16104, 59135, 16434, 42639, 14406, 25006, 45065, 52814, 7259, 21747, 54687, 16546, 19165, 18066, 222, 5243), (23099, 26420, 35150, 16865, 19171, 14037, 43504, 42411, 499, 42613, 14320, 43247, 42000, 57780, 7640, 46245, 11328, 21688, 20796, 39940, 49376, 49871, 55771, 44214, 13977), (6399, 1212, 46061, 34491, 10718, 58624, 62432, 37011, 61248, 7926, 4609, 31575, 30819, 2718, 57545, 55655, 36586, 60193, 8750, 4497, 53351, 52356, 23273, 24101, 10692), (13784, 25949, 63028, 48657, 21298, 24138, 34764, 21492, 16965, 4121, 31889, 23448, 16713, 38726, 51052, 26415, 14435, 26903, 6, 63776, 54118, 37735, 11718, 56278, 28087), (6294, 16120, 1125, 45344, 14612, 7070, 53634, 41145, 48554, 56287, 65523, 52323, 63997, 51622, 60545, 15546, 28830, 7244, 39932, 52456, 29035, 30067, 13416, 55619, 54414), (43392, 47211, 40679, 43956, 27959, 46326, 44565, 52161, 8795, 35238, 49981, 26182, 13553, 28502, 30518, 12346, 19592, 15068, 11524, 13874, 16496, 49614, 37741, 12554, 48443), (35605, 40231, 46523, 64262, 62455, 1478, 64385, 12454, 8226, 62359, 37365, 43197, 46104, 15468, 14170, 11221, 8399, 1971, 13183, 48631, 6083, 61096, 42574, 57319, 42670), (33845, 34655, 51835, 25660, 47295, 45704, 13184, 12026, 63295, 36116, 33105, 52377, 47580, 8158, 57856, 12663, 8161, 38149, 47834, 43270, 15138, 53324, 62016, 14869, 21146), (25896, 16268, 1309, 10875, 52537, 3992, 60509, 31817, 19975, 44669, 34871, 52811, 568, 64789, 42805, 3793, 53004, 9646, 47482, 26673, 17369, 24473, 32357, 8991, 45373), (18840, 63600, 56874, 37866, 64985, 21465, 35120, 27277, 40115, 54508, 22364, 11688, 65376, 26257, 9013, 34469, 60354, 28365, 64276, 18835, 1436, 5187, 59163, 35833, 10641), (53348, 56069, 11816, 55824, 46964, 1467, 56624, 44821, 60699, 17659, 39486, 46005, 26704, 797, 35774, 41074, 4335, 31852, 49186, 5076, 14088, 51174, 15410, 19180, 14703), (44573, 483, 19483, 58607, 46505, 23558, 48199, 41332, 36181, 37223, 45223, 32511, 59677, 44988, 59468, 11608, 31066, 40249, 31975, 52656, 8042, 36342, 7653, 6755, 51345), (18511, 18238, 39425, 15844, 53208, 37649, 39278, 65035, 24792, 18191, 47667, 41177, 2795, 13977, 25188, 61539, 56690, 40370, 42099, 34268, 39279, 54248, 34233, 7062, 40629), (63737, 23793, 2637, 40536, 27120, 14817, 33897, 39542, 28474, 16254, 26802, 40747, 14181, 62578, 38580, 9416, 45077, 49330, 56257, 53446, 50255, 8371, 15783, 14466, 61794), (63919, 5443, 59789, 34151, 47756, 61963, 5836, 49657, 43692, 28483, 59197, 23037, 42306, 11413, 40497, 51321, 27452, 24476, 50381, 32935, 15304, 20455, 6793, 38025, 27094), (54377, 33021, 42770, 10751, 39409, 22377, 17704, 63959, 3921, 60869, 1926, 13690, 55823, 12812, 45165, 36864, 17613, 33678, 35194, 51764, 50702, 26430, 33017, 30530, 29157), (4500, 33873, 16821, 25117, 31072, 53542, 39633, 55081, 13259, 64116, 30057, 18069, 46706, 15328, 48019, 16765, 57823, 60283, 53217, 26007, 21991, 12275, 48684, 10829, 43052), (19399, 15068, 39469, 57818, 35368, 31944, 6239, 55564, 54498, 21423, 35903, 64690, 25811, 49512, 8579, 17063, 53125, 37650, 54902, 19011, 46588, 64443, 53458, 10496, 33997), (36753, 38254, 35046, 29319, 11315, 4625, 9845, 55471, 10825, 4146, 44701, 26891, 64141, 26381, 20201, 50864, 4373, 9568, 57596, 23733, 29816, 62794, 24209, 56241, 61492), (22189, 23661, 44962, 37661, 65172, 64645, 36788, 15707, 44828, 55464, 24287, 64964, 42224, 25075, 37059, 12140, 37498, 36392, 30652, 15022, 15538, 41552, 16012, 44139, 1187), (2122, 434, 35620, 7877, 61163, 25109, 31300, 36700, 60876, 63635, 20378, 64663, 1142, 22044, 10726, 58010, 43188, 53085, 3559, 57975, 20719, 14957, 10090, 59805, 28586), (47707, 696, 47302, 36666, 18799, 1601, 22511, 28652, 17757, 26012, 52662, 37221, 39813, 19036, 9108, 34362, 64315, 59862, 26579, 53696, 2311, 16402, 59221, 8669, 17083), (45664, 27478, 27405, 47366, 38305, 53909, 47049, 28142, 58776, 27099, 14278, 49777, 64629, 64549, 15050, 21231, 17190, 59355, 44853, 47295, 5956, 35987, 16014, 65521, 8640), (6479, 1540, 53973, 9556, 34233, 41022, 30539, 11423, 11005, 62412, 49253, 40761, 47722, 19009, 24958, 60025, 61544, 8526, 26366, 59330, 50658, 64838, 7310, 28530, 2334), (29498, 20313, 34418, 35993, 56417, 42588, 11158, 31656, 54694, 20709, 44287, 54682, 30062, 14131, 48035, 34634, 11862, 2102, 47380, 16232, 9549, 21473, 13191, 61240, 20271), (9601, 61049, 24213, 19261, 53792, 50407, 61296, 17416, 50976, 61000, 21631, 16559, 28624, 51856, 33824, 22565, 22355, 40642, 55526, 23085, 12943, 49930, 10531, 52853, 34356), (64352, 56398, 58728, 61381, 54473, 56551, 14978, 5009, 6361, 28604, 5976, 43087, 15155, 41930, 22922, 46937, 30621, 52629, 5259, 14654, 31960, 19707, 50238, 49263, 1705), (41072, 37498, 64937, 6495, 1520, 44745, 28575, 25464, 31082, 8866, 11761, 4958, 3675, 27760, 22072, 56788, 606, 14188, 8598, 35894, 2447, 32266, 26085, 42112, 29542), (54819, 28208, 39652, 24095, 7646, 50084, 24108, 9501, 31881, 19725, 9481, 47582, 42615, 50020, 49246, 6909, 20243, 10922, 65085, 61318, 17831, 18341, 8565, 59013, 22519), (51484, 44365, 26216, 17401, 38117, 2951, 42265, 16995, 15512, 15862, 21479, 37165, 46796, 30355, 24936, 16265, 27371, 26654, 31054, 30072, 59341, 27201, 61868, 13299, 51766), (33157, 62613, 56051, 38993, 8471, 41519, 49324, 12476, 14398, 27275, 25152, 34547, 17576, 26953, 56420, 41987, 63769, 24998, 63202, 13236, 19281, 12898, 57457, 47309, 47987), (44202, 1590, 5520, 29268, 54269, 64520, 22572, 27179, 970, 38611, 13925, 61680, 999, 49242, 14446, 51390, 11206, 16950, 16277, 26393, 11206, 46242, 61531, 52116, 27927), (57928, 3423, 20760, 8379, 60064, 9052, 37975, 44550, 20437, 12638, 24077, 46488, 655, 39941, 49454, 62020, 9911, 2126, 21860, 25548, 55822, 12128, 65458, 6236, 12981), (29134, 29271, 23339, 36030, 8335, 8000, 30417, 58188, 64028, 37745, 23901, 6134, 3443, 45373, 17677, 64446, 37318, 30881, 1545, 19574, 4300, 50531, 29845, 30373, 16658), (35197, 24220, 16615, 14708, 57713, 37798, 48494, 43315, 61503, 30667, 3572, 17415, 17926, 15960, 10934, 41062, 588, 15757, 53295, 23747, 37738, 21923, 19027, 52135, 14894), (35901, 20938, 52967, 59895, 32392, 56526, 63764, 10882, 6221, 47023, 7819, 44359, 48463, 57552, 19487, 870, 37789, 24544, 8665, 6796, 37008, 11084, 37071, 37446, 37477), (33581, 9710, 58585, 33477, 52962, 55240, 55682, 52775, 55470, 14493, 29339, 53026, 2246, 45631, 48503, 52770, 64953, 14615, 40850, 43213, 19488, 9934, 36379, 19369, 23062), (53433, 31354, 26729, 4737, 36088, 9556, 39322, 41664, 12281, 17538, 19634, 24009, 39349, 59567, 39317, 45612, 13337, 49526, 2949, 63302, 19332, 16142, 42893, 22500, 31447), (64343, 20448, 24056, 7726, 23523, 47991, 21312, 49127, 28767, 15645, 7959, 10844, 35030, 58296, 24518, 1786, 53695, 51978, 11251, 63390, 54699, 42020, 34624, 59420, 41142), (20583, 14708, 25263, 45546, 15066, 48301, 43891, 269, 27526, 30263, 48686, 50198, 52414, 16563, 16818, 60277, 31314, 40755, 1052, 5180, 36841, 16298, 22102, 6460, 39962), (20237, 10039, 30465, 21473, 2037, 15773, 30226, 36800, 12140, 28784, 6634, 15444, 28948, 46045, 52074, 55100, 31429, 45290, 55316, 49162, 53405, 48906, 65080, 26484, 64677), (50960, 57786, 34540, 30892, 50499, 53269, 36928, 37472, 4159, 43905, 7923, 28785, 13450, 47171, 3914, 30482, 63341, 20474, 35907, 32291, 19621, 26253, 30589, 55942, 50779), (57887, 4687, 38046, 15985, 27517, 3176, 30459, 19945, 48858, 12318, 23117, 14227, 53964, 47342, 51146, 28792, 64125, 22471, 9428, 1302, 30201, 40223, 5317, 63472, 11285), (4845, 11678, 2789, 33554, 41212, 20306, 22631, 6850, 26043, 19695, 46369, 63520, 30036, 12960, 50350, 10218, 53339, 49247, 1826, 1867, 65229, 7161, 33754, 59708, 20449), (27264, 10788, 57987, 55996, 23595, 56582, 20511, 6185, 53863, 55400, 46001, 52404, 10867, 56049, 11926, 46715, 4113, 55196, 42200, 58309, 12156, 64210, 15908, 10723, 24839), (4191, 44116, 10718, 38556, 29366, 33671, 32416, 25247, 3188, 4755, 50893, 60395, 30519, 5171, 46432, 63033, 20200, 17562, 34477, 32951, 20175, 17649, 2093, 17238, 58019), (18543, 3552, 53296, 24168, 56524, 62453, 3836, 35938, 43630, 37176, 53822, 32927, 52252, 57838, 9739, 24869, 40132, 40548, 10321, 9320, 60737, 19541, 155, 2719, 54383), (44200, 54899, 18220, 37752, 4967, 53953, 63730, 8668, 46791, 32391, 20703, 63062, 15403, 8838, 18238, 64706, 43579, 965, 30179, 12809, 42392, 38147, 59588, 50704, 31645), (22546, 34193, 16626, 14039, 7066, 35879, 4941, 5365, 18574, 55579, 22151, 265, 64669, 51358, 17427, 62416, 22595, 61936, 36119, 32721, 45386, 3542, 55720, 24601, 45799), (43097, 60529, 47152, 41891, 64622, 13055, 30231, 4555, 51974, 8146, 16936, 1917, 41399, 30888, 10075, 9160, 53293, 20574, 4619, 2991, 5239, 33018, 56598, 7261, 8789), (29832, 49059, 52393, 46480, 19345, 44070, 10612, 31778, 31501, 4741, 64845, 19162, 9637, 55922, 5024, 27372, 17223, 16041, 58082, 41608, 36057, 14235, 26581, 51856, 5254), (19473, 65302, 1495, 25996, 30360, 12547, 23701, 35656, 2306, 46937, 40991, 11936, 12127, 6463, 35501, 10515, 28103, 13887, 55180, 6764, 62446, 50656, 13493, 18229, 13356), (11989, 55345, 34906, 50967, 20697, 38188, 31056, 17826, 21389, 61224, 27108, 27066, 24181, 13520, 23364, 60542, 19385, 35120, 6873, 57551, 1920, 48390, 4063, 32893, 16), (60018, 47011, 204, 59310, 15419, 19266, 45227, 24399, 8811, 13756, 52827, 54637, 55745, 42389, 47570, 33479, 13416, 24485, 18581, 56926, 9898, 30276, 2727, 2680, 42558), (26062, 16474, 18617, 54588, 62791, 16362, 60899, 22482, 62910, 47603, 25213, 55066, 16867, 56378, 28283, 16993, 2577, 56773, 31101, 45924, 40700, 30243, 31725, 38652, 52094), (31137, 30052, 53675, 27162, 1747, 23364, 1232, 57573, 63764, 9988, 13462, 49834, 26414, 10583, 23560, 36480, 6528, 27315, 40965, 25839, 25162, 11241, 24099, 44973, 63006), (43598, 6595, 49763, 15926, 54795, 61327, 27144, 5926, 28751, 25066, 47030, 54998, 49476, 1985, 55010, 65514, 30528, 24000, 15566, 53043, 54363, 55221, 47656, 3516, 15968), (51304, 24276, 35797, 4532, 53107, 58071, 53335, 3077, 18341, 64517, 2030, 49772, 32830, 56224, 63310, 40939, 56753, 61707, 62727, 1707, 6176, 11754, 57781, 38537, 22589), (10808, 8890, 63023, 9752, 3458, 10047, 36169, 4885, 15659, 48724, 47614, 59642, 60442, 64037, 11253, 30094, 25309, 45477, 62074, 45371, 58769, 37473, 7088, 28835, 30768), (53479, 23226, 29078, 7185, 36072, 62161, 26497, 22940, 44485, 58654, 59709, 50915, 46680, 30964, 11721, 58839, 15932, 31588, 1643, 47285, 56018, 41764, 65423, 24587, 51258), (24579, 54314, 36357, 15517, 50806, 27523, 7198, 41316, 438, 3466, 16417, 31165, 37966, 27325, 40635, 39457, 29974, 29351, 4717, 14305, 21841, 22695, 35556, 4623, 35333), (14145, 20983, 15785, 5159, 31843, 32503, 48088, 19272, 17639, 47969, 38111, 46404, 27021, 27163, 40992, 32640, 10631, 58771, 21183, 55259, 37570, 38600, 24101, 43802, 57268), (30535, 55382, 51790, 65386, 61313, 27009, 47348, 54706, 29345, 57975, 59510, 33283, 12304, 38485, 27854, 42653, 37122, 28343, 62150, 31879, 38341, 48393, 63731, 4580, 1109), (45444, 13078, 47185, 63605, 7407, 4334, 10466, 35410, 47371, 64790, 23651, 58112, 52632, 31865, 36880, 20129, 13196, 42751, 10019, 21009, 33346, 56968, 16165, 15206, 39504), (1219, 55005, 33701, 52885, 59626, 13366, 8447, 13329, 26967, 9617, 42485, 59096, 53649, 22607, 37379, 64470, 17061, 2242, 10197, 54104, 59288, 52121, 15309, 41970, 40246), (39508, 43080, 7848, 13136, 4780, 19837, 18665, 36829, 59185, 14498, 31951, 27579, 27642, 20224, 46712, 45286, 55167, 8667, 29901, 27122, 16165, 42747, 58551, 31235, 32183), (45707, 38719, 36815, 6879, 30558, 22898, 13691, 2300, 55201, 59990, 29705, 14450, 37257, 28887, 35902, 31849, 54982, 55611, 59639, 15908, 38530, 45482, 57002, 17773, 45730), (62021, 58401, 17579, 6417, 5135, 50093, 29279, 63562, 27849, 14624, 40420, 52121, 17163, 30438, 59789, 18376, 7746, 52363, 62553, 13032, 62220, 19809, 52254, 2098, 59282), (62493, 61647, 1926, 29120, 43100, 16998, 41266, 18718, 64362, 64064, 45443, 33656, 57598, 22626, 22080, 65148, 40538, 40040, 19069, 55032, 52555, 11510, 32425, 50772, 46211), (40803, 2773, 31433, 3309, 58410, 21744, 55647, 31192, 1046, 60950, 22313, 4743, 64606, 18215, 42874, 23846, 56122, 2195, 62198, 41788, 45712, 19626, 57164, 42436, 64465), (36368, 24800, 22506, 51673, 62864, 62363, 14848, 13531, 47741, 54656, 24671, 25068, 22645, 17549, 2028, 5926, 49775, 5422, 59820, 29867, 43471, 26193, 46524, 10141, 64570), (31805, 52969, 56561, 47888, 17215, 9773, 60022, 56381, 30297, 5195, 2496, 58131, 52640, 37647, 10996, 60211, 52083, 45669, 8017, 15569, 59443, 9148, 940, 6163, 5303), (63300, 585, 25333, 36089, 48961, 61153, 50554, 56821, 52443, 39873, 56484, 16733, 53382, 34124, 34907, 7765, 43127, 6779, 52300, 10118, 25321, 28876, 17177, 50337, 51315), (48165, 55490, 52266, 56535, 39226, 11789, 15117, 60668, 30404, 48325, 414, 22460, 25112, 61371, 46061, 13736, 46151, 4199, 11284, 41663, 60761, 43235, 37089, 37715, 45975), (24640, 16563, 50500, 62927, 58652, 46050, 51168, 55386, 22623, 60594, 43859, 46831, 48574, 17377, 18753, 44020, 30142, 26084, 24454, 55198, 41207, 46533, 4890, 64327, 567), (11905, 14146, 13555, 4639, 39965, 7133, 60113, 20299, 60764, 26710, 30328, 37973, 8736, 50336, 26853, 31923, 50957, 34096, 14998, 27602, 22115, 33284, 7474, 50537, 61184), (57095, 14078, 50459, 58839, 38690, 10149, 1270, 63037, 21592, 33211, 22715, 30312, 59778, 52192, 11410, 47463, 44306, 28062, 8127, 61444, 30819, 52504, 2280, 13173, 21883), (28002, 12306, 37574, 42363, 24697, 38318, 43166, 12468, 11769, 7603, 39355, 10085, 23862, 30533, 3870, 43629, 54085, 17822, 29085, 56024, 48215, 2856, 63543, 25306, 56316), (11165, 40608, 17619, 41345, 62315, 14107, 27414, 10293, 43194, 37317, 33706, 27892, 40302, 57229, 19381, 52201, 18348, 38638, 48042, 24108, 43174, 35660, 12364, 35266, 31022), (65431, 20193, 9566, 1717, 5974, 34413, 25325, 1479, 5896, 46275, 29653, 18121, 2756, 46753, 37842, 63892, 22045, 37685, 22138, 23870, 18115, 45866, 27016, 28023, 17793), (11792, 12428, 62376, 18639, 58505, 31247, 25480, 50819, 2634, 25135, 52265, 12888, 18374, 54119, 62910, 18010, 43899, 14775, 14785, 19883, 54759, 53822, 65233, 13593, 4225), (53095, 18737, 51631, 33057, 48158, 5981, 5993, 10050, 3810, 36124, 44134, 32226, 16377, 23753, 15955, 54085, 12105, 33606, 56549, 56883, 48277, 51042, 42694, 29299, 38955), (35530, 36974, 27769, 18370, 16640, 21320, 65238, 38088, 56090, 46654, 51091, 34856, 23008, 40052, 40167, 56590, 55441, 60227, 29597, 62672, 61219, 27385, 23299, 34897, 38540), (27000, 22157, 19146, 40435, 61938, 45106, 57876, 29202, 54095, 63743, 58981, 46861, 55535, 63048, 48488, 60554, 49144, 38301, 23682, 63503, 14032, 6367, 42334, 64792, 5323), (56215, 28393, 16004, 35290, 46141, 23712, 12606, 40011, 6712, 14539, 52877, 29295, 53409, 17778, 999, 23886, 5953, 4222, 42071, 65490, 30649, 3234, 7893, 7850, 41844), (51649, 47385, 27315, 19926, 49812, 57784, 7593, 56021, 52273, 46071, 8651, 20519, 63643, 49441, 52394, 45014, 28195, 50957, 63208, 25564, 7041, 40403, 7042, 19126, 20366), (64394, 27123, 18034, 3124, 45656, 35262, 1404, 14605, 42104, 48585, 17474, 59750, 3434, 15797, 19035, 18466, 23607, 43619, 36405, 13782, 20076, 4647, 45588, 39001, 29795), (14144, 19743, 9060, 61969, 58792, 51720, 18869, 46280, 47392, 51070, 37802, 31855, 37003, 42430, 10939, 33540, 55555, 4524, 32804, 21960, 44063, 15613, 53729, 37215, 62294), (17464, 44934, 5979, 61466, 29900, 49802, 49674, 2591, 42291, 43398, 8520, 29710, 5994, 38263, 25534, 49483, 48103, 23489, 48675, 47138, 50255, 4492, 10662, 24991, 19740), (33550, 42594, 56864, 32488, 39986, 4156, 34366, 1155, 52853, 52065, 44096, 47709, 63285, 50686, 36845, 3748, 13669, 21954, 28552, 5628, 9348, 59662, 60560, 11067, 36396), (30710, 51488, 40147, 12808, 323, 8116, 26055, 50339, 27067, 5612, 25283, 34056, 61330, 54673, 19212, 13312, 53930, 36825, 10810, 58231, 54068, 64347, 31033, 2781, 56981), (63093, 51098, 57120, 2545, 13254, 64827, 15054, 58194, 37199, 24356, 45269, 11933, 34767, 33345, 2279, 46423, 35416, 60372, 18528, 6444, 19588, 26012, 38065, 29013, 19252), (56782, 45952, 34278, 43015, 403, 35449, 65316, 25864, 23538, 40134, 25821, 51645, 49040, 61454, 17525, 46462, 58009, 31321, 7272, 42792, 23329, 5820, 24724, 43406, 4892), (28486, 48757, 60524, 2943, 5118, 61453, 49364, 43452, 41766, 13875, 27551, 39465, 62949, 29719, 31446, 61710, 4074, 60121, 36112, 4650, 1376, 36501, 5526, 23258, 11917), (38742, 1380, 24354, 36801, 16178, 38038, 41073, 30667, 8101, 14433, 7593, 4382, 57010, 62351, 63239, 53018, 34957, 46385, 43738, 56474, 35887, 9044, 33924, 28049, 12187), (35026, 29826, 7068, 48114, 37818, 11406, 53102, 49117, 22145, 7189, 65065, 19311, 36075, 13533, 39977, 60094, 7636, 8631, 25030, 47694, 62972, 57467, 42573, 16774, 37748), (14511, 27904, 16509, 17349, 54912, 59810, 24019, 34223, 52550, 15893, 34843, 19918, 60054, 52498, 25105, 3063, 48744, 12549, 30939, 14687, 51683, 17807, 9595, 29249, 37264), (13807, 51198, 41212, 7357, 4834, 9408, 14593, 46990, 27074, 19200, 2371, 43594, 52466, 33055, 28264, 8804, 23777, 65421, 49828, 45959, 62422, 25018, 46877, 52451, 34966), (907, 37645, 58526, 2354, 54693, 2869, 7955, 17118, 48696, 63776, 28853, 33882, 3897, 60555, 2622, 25113, 43973, 8808, 15097, 34124, 44904, 36855, 30353, 27253, 16364), (26049, 62381, 33274, 31697, 55168, 40549, 10999, 51072, 58412, 50211, 61513, 58402, 23544, 36817, 52233, 1962, 20255, 43284, 10973, 61400, 19482, 57805, 39956, 12845, 25140), (42961, 3864, 44461, 45102, 22005, 2845, 16886, 4144, 31880, 44179, 42814, 51550, 59142, 23255, 50068, 64831, 60010, 8109, 51989, 43109, 38490, 60650, 9343, 60654, 9148), (53968, 38587, 4962, 53888, 22619, 16838, 52124, 55461, 5926, 24631, 60607, 46306, 17612, 21616, 54880, 959, 65238, 11519, 15381, 60287, 6053, 58516, 1697, 18722, 44295), (5411, 38574, 60167, 65408, 6036, 34636, 8846, 18036, 58589, 113, 6940, 53867, 37181, 52157, 15203, 22592, 10704, 54970, 28114, 45098, 54680, 21187, 17446, 24002, 16579), (46692, 64564, 59352, 38164, 45080, 46654, 48991, 35837, 20725, 63647, 3606, 63853, 34612, 54250, 21100, 6361, 7356, 44914, 4691, 50918, 25115, 60784, 56854, 65439, 63336), (64989, 38734, 22601, 61882, 8545, 59988, 22135, 12639, 41492, 20050, 6016, 2530, 10238, 24120, 10420, 39747, 46627, 63980, 12182, 34431, 39290, 18018, 44497, 47552, 924), (55830, 40159, 252, 29960, 49498, 57379, 32230, 59538, 62195, 30657, 58226, 26804, 10105, 11513, 14642, 55493, 62605, 6599, 22954, 52546, 54144, 63152, 57986, 54772, 18641), (49093, 59757, 42990, 19532, 20042, 41578, 30774, 62347, 30690, 9598, 47965, 56463, 56323, 5220, 20986, 33614, 37839, 47766, 37748, 42781, 59983, 9466, 54269, 46086, 41695), (43585, 7333, 12821, 17777, 25411, 37960, 43487, 10002, 16800, 32312, 47763, 19146, 57636, 36831, 15344, 683, 11209, 57821, 29739, 53816, 43772, 42476, 6549, 1074, 40189), (64853, 42245, 47372, 490, 12846, 8213, 15840, 43297, 39798, 62096, 63795, 20183, 50077, 6869, 41071, 4653, 34874, 34072, 51696, 36866, 2004, 18996, 29444, 61213, 58394), (37046, 26443, 52443, 12772, 41608, 56488, 15957, 3483, 32741, 1629, 46230, 57175, 16903, 5970, 55901, 2004, 35343, 8376, 24779, 43520, 22304, 52771, 21989, 57490, 40425), (12721, 53907, 10845, 39406, 18937, 29435, 59593, 19223, 54855, 6700, 21921, 54557, 37631, 48234, 7196, 60297, 65302, 6953, 9106, 5414, 24110, 31677, 15889, 38563, 38839), (60629, 57141, 6697, 54731, 380, 58083, 64262, 7828, 56574, 17224, 21967, 34863, 33933, 47622, 21848, 16840, 64791, 8664, 19923, 40325, 46603, 28943, 3906, 39946, 646), (48618, 21741, 12300, 10508, 25457, 48369, 23014, 60313, 29452, 20889, 43589, 17734, 30098, 15802, 58159, 28253, 55249, 27257, 32675, 59426, 20176, 4559, 8509, 65443, 26938), (64738, 42836, 32012, 55006, 57480, 52374, 38391, 15937, 20094, 40601, 1455, 19582, 16423, 20390, 46079, 11518, 22249, 38053, 31044, 7091, 4809, 11675, 24474, 42338, 10320), (9746, 40619, 55174, 6745, 23394, 39554, 59409, 8465, 704, 64830, 51311, 36502, 28727, 21456, 56099, 13446, 16937, 62816, 58039, 62135, 20061, 14400, 35539, 56462, 10078), (57647, 42157, 9908, 28903, 4838, 58084, 46069, 61109, 14638, 10078, 32428, 17519, 61025, 6241, 36949, 23125, 51499, 11415, 63224, 45493, 55821, 9494, 50427, 6089, 50981), (48629, 38912, 25599, 59443, 51504, 34332, 17881, 46187, 2932, 63955, 6765, 51194, 60478, 27771, 22382, 57859, 23622, 28476, 38432, 27736, 31909, 13886, 38244, 17686, 45651), (31147, 26495, 26924, 59568, 40273, 51823, 10210, 22384, 63797, 7201, 34132, 40641, 15057, 34564, 15138, 57696, 32464, 39727, 17133, 64551, 14196, 36197, 64210, 29465, 55654), (8624, 57726, 62330, 33604, 47055, 7238, 53611, 60343, 63968, 17666, 15735, 38962, 31112, 25135, 24546, 40369, 18141, 51773, 52040, 197, 60809, 40081, 64081, 13812, 57609), (39116, 18593, 3763, 24094, 17588, 31585, 26876, 54295, 31877, 22686, 47319, 54515, 23340, 40473, 47714, 50508, 27424, 36753, 58900, 1013, 50158, 1570, 8825, 40692, 43087), (639, 16476, 38997, 59210, 19995, 29853, 27897, 53271, 19195, 913, 10460, 3688, 64737, 24595, 24213, 44686, 63851, 47962, 20031, 43957, 35128, 56447, 25833, 51570, 6945), (55552, 22971, 65098, 43078, 32013, 6335, 63879, 49770, 31365, 36230, 55044, 22024, 57298, 27523, 1379, 40305, 28731, 51343, 34131, 14628, 22560, 55332, 9591, 18207, 61872), (539, 38199, 11560, 12892, 2081, 23775, 12739, 56368, 40554, 15822, 57922, 36214, 38258, 12916, 11690, 62341, 40008, 58613, 1773, 61907, 34867, 21438, 13113, 51723, 50163), (45650, 36054, 9701, 23398, 15793, 59676, 26566, 56694, 430, 47097, 57787, 55058, 3369, 34561, 17427, 49961, 50057, 51949, 56750, 20778, 21981, 61980, 64556, 4590, 29394), (28399, 7215, 60684, 7774, 64222, 37024, 28793, 34398, 64463, 52295, 21001, 36281, 30198, 13328, 63363, 18806, 39086, 51972, 22332, 35674, 20881, 47135, 50635, 59558, 50760), (58774, 48444, 35982, 44995, 20011, 43715, 3242, 53666, 6898, 13300, 46487, 45066, 221, 65247, 8618, 6983, 1292, 61162, 55386, 3867, 28575, 47386, 44186, 52571, 14131), (17590, 29569, 17370, 60537, 51022, 34229, 40322, 23999, 30306, 42915, 9410, 16320, 1499, 14833, 10452, 26834, 28018, 28019, 1731, 35956, 54589, 63186, 36169, 55097, 62006), (10371, 3217, 24235, 19974, 49359, 43961, 6038, 2041, 51541, 27519, 43639, 19541, 52769, 47981, 61492, 30429, 39138, 57556, 64607, 52802, 28936, 20311, 31591, 40855, 17578), (33223, 49962, 56508, 6799, 8915, 35939, 51716, 9107, 61708, 48229, 17619, 27932, 1370, 36706, 42163, 18716, 7599, 44442, 16888, 16413, 55348, 3574, 33156, 59104, 40488), (11674, 43758, 9786, 64306, 4525, 36004, 57032, 35989, 46835, 33168, 9176, 47820, 25442, 31303, 45378, 22946, 4664, 63455, 18682, 24020, 17260, 32108, 47643, 50203, 111), (13151, 33416, 42829, 40239, 25525, 206, 38727, 18861, 10906, 39380, 65242, 7211, 34898, 11083, 1629, 45330, 40209, 26651, 1904, 20045, 29436, 32311, 50213, 17590, 56641), (16004, 13599, 39844, 1233, 58102, 4003, 33943, 4754, 33211, 36073, 1077, 26746, 18696, 40727, 49200, 1999, 63949, 40143, 698, 6008, 29548, 24597, 17802, 45, 36334), (3730, 49122, 45996, 32364, 51038, 35556, 35731, 35632, 29334, 8738, 4075, 49443, 57022, 19089, 60494, 36305, 32103, 34364, 52546, 12875, 9740, 52125, 35067, 8855, 36592), (34722, 38177, 61583, 47674, 34999, 43928, 33125, 31372, 31868, 43696, 31691, 61371, 47424, 2943, 61275, 60426, 34144, 24193, 51167, 47365, 35412, 59688, 5631, 20426, 17465), (25300, 12759, 29572, 2197, 20890, 28993, 2554, 5999, 44311, 39333, 8759, 15311, 32362, 60493, 57165, 45054, 20715, 17084, 2088, 10313, 46837, 2093, 180, 61763, 16621), (23302, 23640, 32196, 44155, 35613, 35675, 12363, 60517, 62169, 12166, 6432, 11265, 38404, 5394, 31287, 5137, 31693, 35866, 64645, 1372, 25262, 8181, 23234, 57660, 15205), (56503, 17355, 48345, 21408, 51201, 62629, 52436, 54993, 28695, 62833, 12366, 65000, 12566, 12831, 13616, 457, 12229, 29342, 15139, 13939, 7349, 36184, 14658, 9127, 62970), (22139, 37536, 28772, 18191, 47723, 10766, 8184, 43, 31899, 3357, 64274, 60620, 44767, 35766, 5922, 11938, 10523, 63452, 17636, 40529, 38506, 41460, 61913, 62018, 24648), (17327, 58384, 8598, 33614, 22357, 2308, 54730, 15161, 54166, 56774, 56583, 15783, 47393, 29447, 54019, 22505, 33456, 41112, 56660, 44933, 26561, 29202, 26109, 12736, 36699), (33823, 24649, 28840, 50533, 28664, 59287, 40051, 41143, 56501, 39260, 30744, 19827, 42608, 26271, 27591, 42231, 41615, 24018, 19784, 48158, 42870, 3211, 41869, 49499, 65256), (18139, 48550, 14673, 60711, 51836, 44499, 28571, 61466, 54938, 14157, 10665, 24865, 31284, 32528, 61022, 45504, 14057, 11290, 62420, 10209, 41507, 49066, 36868, 59100, 34745), (60379, 54941, 2357, 36116, 61350, 51436, 36128, 1666, 4884, 42558, 38813, 25150, 54935, 45856, 28604, 51450, 46275, 65194, 50416, 18510, 12568, 53145, 63241, 60217, 32922), (63114, 65015, 36918, 48938, 42993, 61792, 10166, 36332, 44998, 29899, 19745, 48854, 40311, 46868, 4303, 18334, 47969, 55416, 1876, 34473, 4869, 44526, 22767, 47450, 1539), (28764, 7817, 22338, 56824, 46900, 46546, 50070, 19976, 44258, 20842, 2138, 49540, 58585, 28381, 10927, 25646, 50562, 20895, 59209, 12103, 878, 57871, 24423, 49638, 21152), (35152, 40018, 9434, 29882, 33686, 30514, 63173, 33718, 57739, 35704, 21221, 30572, 35030, 58742, 3746, 48598, 10634, 39186, 51004, 59387, 56350, 30359, 2973, 4675, 65040), (10438, 56454, 52659, 30094, 11537, 45407, 53495, 41606, 37502, 41647, 1715, 26427, 22608, 63180, 36133, 18087, 26983, 57554, 54730, 49178, 35475, 38014, 60893, 52608, 20002), (48140, 652, 35235, 42554, 35370, 12347, 52436, 58033, 23864, 12802, 36052, 1617, 52972, 14200, 1862, 58804, 51704, 26744, 48092, 22939, 35518, 26934, 56336, 11701, 31470), (29453, 4986, 55345, 43240, 55124, 62674, 37113, 24304, 45423, 31452, 3853, 10268, 53685, 48246, 10669, 5181, 35370, 48540, 39830, 4680, 7037, 37041, 52275, 20449, 63888), (62419, 44507, 25658, 48725, 49144, 5134, 39525, 42258, 17853, 32028, 11992, 16158, 46441, 35446, 43517, 6127, 57341, 41877, 42833, 53075, 31294, 9571, 19996, 20608, 20487), (36380, 50578, 37067, 6242, 29594, 63655, 193, 10313, 6406, 19989, 57440, 29924, 5907, 47961, 51420, 5550, 34031, 33155, 62979, 47412, 42139, 44386, 62876, 20699, 52870), (27813, 30843, 50114, 54680, 27403, 14688, 7381, 40849, 51850, 61494, 966, 47731, 34755, 51148, 13844, 13323, 19173, 26086, 42951, 22460, 41890, 53246, 5244, 16633, 53657), (37028, 4214, 46571, 682, 36671, 40301, 20958, 45740, 32686, 11806, 23284, 3810, 3004, 55663, 18929, 11757, 65010, 6745, 573, 9240, 24868, 62836, 24699, 8706, 8414), (8564, 14317, 50707, 51490, 12220, 2273, 28746, 12348, 54405, 48634, 64661, 27716, 34604, 21525, 30902, 3408, 38889, 13340, 62371, 53733, 21018, 24059, 27720, 2043, 62729), (13508, 23824, 28770, 22589, 10559, 53661, 56342, 30949, 22561, 64890, 58993, 35487, 26496, 15908, 47928, 51183, 28839, 57808, 50208, 29200, 24389, 38298, 9497, 12388, 63563), (41317, 40918, 63242, 30438, 56650, 34485, 56180, 8503, 25194, 56821, 28597, 19280, 1725, 18857, 18070, 19445, 48962, 7118, 34477, 23735, 44147, 32363, 54874, 56445, 9375), (10327, 23042, 64591, 20995, 8861, 43987, 34143, 3153, 36160, 39005, 60469, 44216, 60884, 11758, 6604, 20798, 11946, 53801, 43765, 30162, 37655, 37919, 17112, 12274, 45332), (40412, 30944, 35887, 9439, 22921, 30322, 11267, 48729, 37338, 32903, 24089, 25185, 55494, 43174, 36919, 32592, 57854, 55634, 61855, 56916, 11730, 3103, 15468, 36951, 27688), (33826, 38770, 43046, 60838, 64619, 26274, 11503, 20547, 10266, 11168, 38932, 17007, 29833, 45248, 30643, 15543, 39839, 6267, 13540, 28238, 53798, 22444, 14902, 8793, 7725), (45130, 86, 26390, 5007, 25326, 64833, 53042, 20194, 1569, 49929, 26988, 27965, 56376, 55541, 27387, 28056, 22833, 48015, 41700, 60507, 17023, 47081, 56233, 64707, 4821), (51925, 59659, 25270, 11111, 25434, 58861, 2643, 54173, 40056, 20931, 29562, 60296, 16544, 44444, 2256, 2073, 43692, 6818, 36193, 16267, 30606, 3123, 5095, 5232, 46001), (55063, 60666, 52958, 64369, 18377, 734, 35708, 54444, 57051, 9314, 3849, 45283, 42791, 43209, 27265, 34139, 65209, 2238, 22083, 53469, 44002, 10697, 13018, 16431, 16496), (65182, 8374, 48381, 63148, 43414, 27940, 40601, 12900, 40501, 19288, 16703, 28635, 30265, 62119, 8551, 30799, 15742, 13200, 25990, 18990, 8049, 6850, 46060, 34671, 42620), (33498, 24921, 61696, 2598, 121, 6308, 26521, 7148, 43317, 12463, 8685, 32081, 27528, 30272, 54506, 18043, 11888, 4078, 40816, 12409, 27661, 60648, 12241, 17804, 40091), (64563, 55753, 15205, 23029, 4150, 60385, 45097, 2139, 7235, 56113, 43594, 45738, 15185, 53807, 41441, 30797, 48511, 30729, 34659, 31847, 13403, 44982, 41261, 40048, 54013), (49825, 10307, 21680, 63047, 7349, 62617, 61106, 41928, 8187, 44472, 28442, 50126, 47071, 63172, 55244, 9090, 29603, 60989, 15987, 58339, 39264, 53001, 35911, 53076, 52539), (21480, 19418, 27677, 15409, 59432, 32980, 7675, 35185, 57867, 40097, 27755, 58451, 64970, 18601, 24789, 10611, 53803, 54080, 25328, 65072, 35253, 22835, 20373, 3774, 46332), (21444, 16704, 41788, 53804, 41790, 48287, 43660, 10494, 2456, 12012, 58875, 11174, 2977, 52129, 33710, 55448, 5116, 11440, 40909, 34498, 4189, 28422, 20482, 34308, 62807), (20879, 7473, 55740, 33169, 30651, 12084, 18625, 48523, 17629, 6779, 52717, 32363, 37238, 15599, 9234, 36450, 3207, 6730, 25625, 8335, 7291, 12550, 9432, 12141, 62104), (15772, 43090, 25192, 24302, 61234, 65221, 7658, 59186, 29259, 49446, 55283, 10570, 53203, 41685, 53169, 25129, 35909, 31853, 15524, 15553, 18234, 29103, 35911, 1679, 10625), (52985, 33011, 1349, 57191, 47918, 4333, 35305, 33775, 39171, 26471, 44081, 15400, 56465, 36574, 12143, 64037, 56513, 63645, 16999, 47033, 53806, 31178, 33577, 58267, 208), (41326, 52945, 31473, 38934, 33849, 25190, 38964, 37053, 60552, 959, 38782, 30020, 34187, 39070, 60098, 24382, 48887, 21373, 35300, 40100, 58512, 13878, 56510, 5909, 20563), (15735, 5533, 59780, 46975, 53637, 47935, 39961, 6934, 35588, 19318, 13583, 13518, 45830, 47378, 21020, 41516, 1024, 27606, 47388, 52350, 7507, 24193, 60391, 27047, 38725), (3940, 58610, 11366, 65101, 64164, 8402, 24612, 18944, 3585, 41475, 24297, 45391, 26763, 38377, 1329, 64078, 21468, 9344, 779, 4091, 36868, 35255, 34373, 48655, 35088), (48721, 45499, 59213, 21814, 2364, 10166, 29895, 46414, 53632, 58153, 28109, 10763, 51625, 104, 32429, 29595, 51965, 52491, 13130, 36553, 24482, 19377, 3501, 48832, 19286), (62098, 49746, 44012, 37172, 49406, 50735, 17665, 4346, 17617, 65267, 26139, 40351, 18371, 33715, 62570, 32195, 43353, 43487, 57279, 14427, 927, 49121, 33383, 6389, 53095), (65264, 62790, 45101, 22186, 24554, 1565, 9649, 39637, 27106, 41747, 33474, 35708, 15445, 12630, 64713, 12945, 11779, 3197, 52523, 35539, 48810, 447, 47969, 17128, 36413), (35329, 5228, 19003, 62052, 18397, 49443, 20378, 32490, 6074, 25966, 53812, 29218, 39645, 60583, 8922, 37578, 55121, 11063, 33622, 52168, 60236, 25858, 4147, 7625, 17965), (51693, 12669, 803, 30942, 56038, 46161, 31328, 231, 6133, 21491, 4068, 31995, 31055, 64821, 1145, 13763, 52228, 40063, 16656, 4023, 2453, 16528, 16395, 39998, 23279), (7901, 26673, 23798, 47144, 38088, 62307, 39041, 38747, 41064, 33271, 8193, 59351, 5603, 17565, 7078, 43830, 58420, 37442, 25460, 8510, 37681, 8286, 47274, 32967, 1361), (8928, 1982, 37264, 28546, 14249, 1170, 6158, 34984, 39279, 62776, 10509, 46165, 50456, 33384, 34909, 30638, 45417, 33202, 16892, 53007, 53042, 29596, 17731, 50070, 38934), (5365, 32000, 18420, 31282, 11948, 60917, 10774, 35499, 26682, 16627, 18312, 16331, 11995, 4049, 12802, 50051, 2137, 64322, 18734, 2623, 22908, 23914, 63943, 44327, 10564), (47967, 51042, 1063, 5874, 41500, 16470, 14662, 34258, 29493, 39598, 56192, 50362, 53022, 64376, 46379, 43744, 14746, 18686, 49601, 28669, 39536, 38975, 51537, 31736, 24331), (37920, 42251, 51847, 58922, 61939, 17764, 11013, 60580, 12153, 43799, 25393, 13821, 46245, 31938, 48703, 4816, 51019, 55376, 37527, 52242, 56868, 21636, 5942, 43823, 29986), (57400, 33806, 39667, 51219, 41460, 11624, 60932, 6626, 31106, 49680, 5616, 9481, 31341, 64409, 39701, 49605, 19492, 8886, 52072, 44449, 3775, 18487, 63176, 64827, 12468), (52847, 10630, 61217, 3340, 23632, 15794, 4313, 70, 29002, 44264, 12838, 6167, 49818, 12960, 40490, 19569, 32087, 52310, 5104, 44508, 32366, 41374, 36207, 62710, 19683), (40855, 51098, 61807, 56767, 11605, 55492, 44769, 17157, 55883, 25144, 14786, 56907, 15775, 50114, 54384, 63813, 33319, 7599, 42500, 38057, 52202, 48986, 43628, 25072, 55294), (8692, 11685, 33418, 25500, 35779, 33369, 53122, 26318, 50024, 513, 43138, 28335, 1125, 32834, 49909, 51939, 22116, 51285, 1079, 20085, 40771, 6206, 35893, 42478, 45992), (54195, 59637, 41308, 63939, 15375, 50398, 57156, 9050, 62478, 10564, 59199, 28716, 39709, 18920, 41988, 21113, 12969, 7174, 30110, 25887, 34802, 64204, 16654, 50956, 37391), (12382, 5582, 51552, 27009, 29792, 5465, 39610, 34643, 7445, 57211, 3771, 54617, 38343, 23587, 20035, 17190, 40369, 27372, 8035, 8701, 21422, 44806, 21261, 44298, 42759), (29964, 24637, 9692, 16698, 35728, 38773, 23095, 4281, 59023, 42704, 28560, 58757, 36087, 3893, 31645, 64467, 20347, 25854, 53633, 57812, 44002, 7152, 26664, 13034, 39235), (63968, 24302, 5960, 59289, 52848, 18882, 18670, 47082, 19571, 13558, 13093, 65028, 26036, 43529, 39195, 23277, 9393, 15869, 1828, 47883, 12478, 923, 42765, 16150, 60034), (45410, 2854, 63576, 22111, 49166, 15323, 24559, 28193, 13277, 37025, 46466, 16069, 4706, 4894, 27900, 16917, 30527, 60520, 16671, 25054, 52572, 41565, 17899, 65408, 49554), (19223, 41368, 4535, 21403, 21973, 14350, 54121, 25290, 30626, 4290, 39185, 50967, 33564, 29405, 9896, 14745, 34854, 64476, 62560, 59510, 23219, 13999, 60301, 44603, 54519), (15837, 37732, 17623, 64721, 43424, 27057, 24573, 42846, 16814, 49782, 18578, 50830, 62572, 21200, 27609, 43847, 36508, 51106, 40822, 16682, 38696, 34841, 60706, 61029, 1743), (14399, 51103, 49671, 9714, 9137, 41792, 29933, 24013, 30136, 55028, 47559, 24243, 49062, 22923, 60378, 55215, 35577, 19071, 19442, 15445, 3725, 7554, 10320, 42365, 50918), (6457, 19918, 14520, 5695, 24028, 45944, 19217, 16666, 5538, 30783, 14918, 54215, 6861, 10595, 4889, 52017, 17416, 38688, 35696, 2764, 58196, 20874, 8442, 21629, 10234), (4901, 31038, 54842, 6993, 14700, 45372, 20423, 61549, 6139, 44339, 21732, 33845, 65419, 35364, 14795, 34339, 2928, 60612, 1748, 7490, 43442, 25167, 6274, 56968, 42498), (13442, 6678, 35337, 64004, 33898, 40461, 35354, 51665, 33337, 36175, 48165, 45335, 11454, 38822, 44056, 16749, 11938, 12779, 31961, 19682, 26000, 1035, 61408, 40395, 58077), (10528, 11295, 49498, 49764, 54699, 52841, 27423, 27692, 46941, 19256, 3575, 43111, 58025, 15125, 45230, 20597, 22409, 13472, 46198, 3634, 2330, 2649, 35969, 9741, 59794), (57942, 52943, 20744, 11399, 3056, 15620, 17375, 9404, 16544, 51167, 23857, 64622, 6904, 62482, 5476, 38500, 33655, 58110, 36382, 12247, 58960, 59808, 42953, 37305, 851), (18760, 58499, 12037, 40754, 673, 65468, 317, 38925, 6851, 44669, 6071, 34069, 8377, 10725, 4754, 6262, 18890, 1152, 18816, 4402, 55082, 34299, 18145, 29150, 23527), (47389, 14949, 44758, 34041, 56449, 52559, 63736, 14126, 20975, 42313, 46369, 8668, 28749, 29647, 64139, 48154, 1893, 36105, 40608, 49352, 45569, 1755, 22758, 23347, 42833), (62208, 48866, 37461, 64231, 37966, 58062, 14541, 21389, 46633, 42987, 20605, 24987, 44944, 45318, 6841, 31789, 34928, 53276, 28333, 54738, 1188, 19326, 7257, 12776, 60560), (24067, 25711, 45810, 56775, 19650, 38142, 24904, 41042, 15759, 8313, 29000, 29685, 51693, 9405, 26242, 21087, 61433, 29000, 32881, 7946, 27879, 45055, 28938, 14805, 41050), (61110, 12541, 32233, 20329, 60930, 10946, 6452, 10751, 53809, 18056, 35280, 22917, 46024, 35593, 30260, 12909, 37614, 15790, 5100, 58556, 49378, 50699, 5948, 35774, 22655), (36040, 60462, 3164, 2137, 14304, 34193, 37257, 38998, 23258, 24117, 45996, 35613, 63245, 18166, 16487, 15583, 61069, 19689, 64406, 64075, 17487, 58614, 7051, 5848, 50631), (61729, 53681, 47545, 28744, 52663, 17933, 16930, 3281, 25719, 50046, 62960, 48131, 35822, 15430, 13996, 33219, 61679, 9923, 8025, 2128, 8729, 41276, 62753, 1136, 42778), (14394, 11126, 28650, 63291, 65399, 58264, 60817, 45389, 11212, 36242, 24620, 52865, 55021, 42086, 4252, 32689, 50573, 58039, 63885, 48584, 35000, 2911, 374, 18079, 53262), (3769, 62868, 47984, 54177, 48876, 1887, 46228, 54306, 20195, 27794, 53594, 62696, 36949, 39106, 29120, 14849, 58758, 8003, 47246, 26419, 25626, 59938, 55706, 47343, 50678), (7021, 13808, 46420, 16268, 10572, 32380, 6401, 34145, 18814, 30163, 26088, 23907, 4065, 32479, 59254, 59530, 28894, 44249, 1822, 29418, 42255, 42921, 42825, 23428, 2179), (47859, 43925, 50252, 57599, 62671, 49562, 11713, 19608, 30797, 42869, 16279, 65448, 8817, 28348, 57485, 10206, 8575, 58125, 40544, 39903, 36477, 38081, 21069, 61709, 931), (44725, 27389, 36543, 33035, 7949, 2122, 62120, 63010, 48270, 41213, 27651, 23037, 47211, 59639, 34808, 12920, 46364, 54882, 15746, 19222, 13393, 47210, 3507, 23216, 54610), (34238, 44068, 11029, 45988, 61663, 41806, 52025, 149, 356, 57229, 2111, 50553, 20448, 49964, 1663, 58358, 18549, 8276, 16324, 22151, 6716, 21132, 36170, 14708, 62661), (44161, 42838, 24786, 51725, 41790, 12964, 30983, 29751, 60378, 61296, 22664, 19479, 48307, 57772, 180, 64406, 16790, 17046, 42570, 11472, 49176, 54687, 10300, 64603, 63948), (56860, 55834, 17838, 2466, 44953, 65427, 39517, 10130, 52008, 24548, 45676, 6662, 56109, 60149, 41616, 47933, 56672, 63565, 61057, 7171, 48242, 57889, 732, 7303, 33775), (24716, 15787, 40267, 24350, 34408, 53993, 14370, 36418, 37434, 18513, 51954, 3744, 22650, 55014, 18589, 47507, 3708, 52556, 6527, 36632, 63975, 23233, 30912, 65137, 55937), (58721, 37423, 28105, 1180, 64142, 14907, 65103, 44286, 12223, 13270, 13569, 15399, 23544, 14691, 4712, 5898, 2134, 15746, 26017, 4381, 15214, 44797, 119, 17170, 33655), (27703, 24488, 52826, 38106, 61871, 36204, 61619, 52441, 47943, 40509, 21140, 6008, 7950, 15304, 30091, 52240, 64497, 39026, 15756, 58906, 43869, 39114, 29924, 39932, 51976), (58533, 34010, 62560, 37596, 48414, 8955, 51449, 4198, 26574, 49689, 62845, 48955, 26314, 1609, 15030, 58739, 57509, 25457, 25794, 31837, 10544, 5816, 52749, 32611, 32898)]", "b": "(11852, 40039, 61221, 5696, 17099, 14562, 55346, 24521, 416, 35663, 23856, 24647, 13107, 7521, 51455, 58642, 33535, 44484, 37656, 48854, 42195, 1308, 63347, 59701, 28030, 31542, 26059, 50134, 55345, 44748, 3842, 33871, 16793, 6286, 39608, 5457, 20485, 3567, 8168, 34256, 25223, 6415, 20080, 30336, 8848, 59707, 13262, 29709, 14596, 62602, 63386, 3827, 19507, 12452, 24685, 54285, 52438, 28929, 56574, 28561, 25717, 23923, 61018, 58933, 27128, 25843, 13247, 39971, 10576, 39854, 61019, 38557, 53816, 10965, 17248, 57949, 7647, 18572, 39844, 43080, 37216, 54036, 18092, 51799, 29800, 3831, 32640, 52752, 54334, 47114, 23999, 63426, 35409, 6725, 35138, 611, 6343, 32554, 47441, 51995, 20627, 34208, 59523, 15423, 60577, 8577, 56130, 47819, 14444, 56929, 38101, 9739, 29166, 28463, 12652, 22462, 35326, 13440, 59746, 1207, 43882, 24120, 27102, 52356, 31830, 15592, 44657, 48958, 32867, 8892, 46502, 21090, 52511, 32619, 22922, 48915, 21674, 64327, 51958, 46676, 12863, 10512, 16039, 30091, 59779, 34719, 14311, 50715, 29678, 44376, 29631, 56860, 48974, 20037, 26098, 5284, 27542, 47172, 43764, 18451, 3263, 25830, 2926, 28343, 58647, 16515, 15335, 58666, 29106, 1406, 33913, 37911, 15982, 34556, 10982, 27882, 27757, 29930, 38500, 33448, 38453, 9745, 18200, 41092, 42055, 9758, 52276, 17265, 19940, 11277, 21090, 6473, 45768, 24909, 24577, 20043, 57739, 64145, 42296, 57394, 35014, 7510, 27676, 33453, 50441, 12646, 56144, 27805, 40516, 3166, 4649, 15125, 3329, 61754, 31426, 62120, 64994, 49076, 40920, 52502, 27858, 44887, 33034, 18523, 20572, 48449, 17993, 31161, 38692, 46532, 43382, 31086, 52760, 58239, 20511, 63662, 34385, 64754, 31340, 7817, 7925, 62468, 14102, 8897, 57085, 21282, 31424, 23070, 16375, 5081, 59000, 62711, 1559, 10184, 26565, 18232, 49036, 28899, 24721, 48155, 39456, 22957, 48313, 14579, 35483, 20248, 4218, 15647, 29873, 43251, 18108, 5607, 16129, 46448, 30421, 46554, 4355, 48089, 39527, 14731, 33222, 18328, 12914, 30188, 59710, 1168, 15763, 28014, 16019, 62362, 33445, 52360, 26174, 25300, 46178, 58779, 9457, 47277, 57732, 22475, 24157, 65435, 36452, 1248, 64663, 10301, 56700, 10176, 8436, 13027, 14493, 16129, 54871, 64243, 36832, 64269, 25810, 60247, 14368, 26154, 17881, 20932, 39373, 51088, 51334, 54154, 32771, 57346, 4199, 59130, 34447, 53487, 15647, 3160, 65020, 19196, 62035, 45262, 65128, 62302, 57896, 62398, 24696, 37237, 52966, 41938, 61626, 53222, 47046, 22868, 3294, 40114, 49910, 2997, 16339, 24335, 8406, 29568, 51388, 13031, 20114, 20393, 38655, 17408, 56918, 8070, 56300, 37248, 32428, 3535, 56734, 53590, 34975, 25470, 63388, 32317, 33244, 58451, 57760, 19552, 5913, 35267, 58273, 33286, 9758, 18038, 13483, 18722, 15900, 65430, 64453, 20836, 35913, 63476, 21980, 2640, 174, 15632, 58250, 50263, 25277, 20557, 21974, 44194, 4401, 44431, 111, 55798, 34275, 23980, 21805, 12520, 29968, 32463, 20932, 62738, 126, 61414, 49719, 62041, 7973, 63793, 44161, 39931, 57845, 5248, 3353, 59633, 25634, 34262, 38935, 55423, 57017, 35859, 32984, 34761, 18603, 8280, 62355, 54037, 35031, 34161, 21867, 11730, 40771, 24174, 43433, 21832, 22219, 41759, 45711, 52981, 322, 48561, 23634, 43810, 51549, 12411, 30193, 43445, 62341, 30797, 32034, 43668, 18076, 42291, 58967, 2507, 3694, 34995, 43204, 55921, 28421, 32042, 32041, 29489, 20959, 3591, 57503, 46729, 6756, 4001, 27079, 21977, 41714, 27990, 32042, 41630, 188, 58107, 56671, 37021, 55834, 28330, 30198, 14634, 26376, 54094, 9778, 47259, 52172, 413, 57322, 32947, 24301, 40103, 47805, 63460, 45027, 58687, 29368, 50857, 33177, 56299, 22794, 34339, 1352, 34550, 2809, 51218, 30240, 13605, 61472, 61264, 46662, 49333, 15947, 49470, 13229, 10793, 27146, 11497, 61800, 26086, 16123, 5144, 25205, 51901, 23717, 34252, 31111, 19235, 20281, 12791, 4478, 44855, 15024, 32110, 29904, 24536, 44187, 64477, 14582, 6203, 36710, 19553, 51294, 35794, 32941, 28169, 33228, 39747, 54759, 52243, 970, 35198, 5045, 21100, 21560, 65239, 9032, 21242, 35101, 34463, 47540, 37675, 51999, 32603, 20893, 48324, 56325, 47725, 30794, 26058, 58492, 37103, 26744, 36667, 57968, 4879, 18033, 44946, 35929, 15560, 37254, 16685, 42421, 54565, 53191, 47432, 23308, 30977, 8870, 50576, 61308, 38765, 52591, 59677, 36136, 26062, 37722, 36608, 34034, 51084, 39613, 57142, 5221, 35690, 37847, 30269, 30642, 34530, 41738, 53860, 62063)"}

LWE，b给了，还差个 A

AA = A*D*PM，其中 AA，D，PM 都给了，A 可求

exp：

from sage.groups.perm_gps.permgroup_named import SymmetricGroup
from sage.all import *
from random import choices
import json
from Crypto.Util.number import *

q = 65537
Per = (1,23,2,13,3,16,15,6,22,18,14,4,25,11,20,24,21,9,5,17,7,19,10,12,8)
P = PermutationGroupElement(Per)
PM = Matrix(GF(q),P.matrix())

with open('output.txt', 'r') as f:    
    data = json.loads(f.read())    
    AA = eval(data['AA'])   
    b = eval(data['b'])
with open('D.matrix', 'r') as f:    
    data = json.loads(f.read())    
    D = eval(data['D'])

AA = Matrix(GF(q),AA)

# print(len(list(AA)))
# print(len(list(AA)[0]))

b = vector(GF(q),b)
D = Matrix(GF(q),D)

A = AA * PM^(-1) * D^(-1)

def primal_attack2(A,b,m,n,p,esz):
    L = block_matrix(
        [
            [matrix(Zmod(p), A).T.echelon_form().change_ring(ZZ), 0],
            [matrix.zero(m - n, n).augment(matrix.identity(m - n) * p), 0],
            [matrix(ZZ, b), 1],
        ]
    )
    Q = diagonal_matrix([1]*m + [esz])
    L *= Q
    L = L.LLL()
    L /= Q
    for res in L:
        if(res[-1] == 1):
            e = vector(GF(p), res[:m])
        elif(res[-1] == -1):
            e = -vector(GF(p), res[:m])
        
        s = matrix(Zmod(p), A).solve_right((vector(Zmod(p), b) - e))
        
        ss = vector(ZZ,s).list()
        msg = 0
        for i in range(len(ss)):
            msg += ss[i] * 65537**i

        flag = long_to_bytes(int(msg))
        if b"SCTF" in flag:
            print(flag)
            return
        
m = 625
n = 25
primal_attack2(A,b,m,n,q,2^8)

W'Blog

SCTF2024

不完全阻塞干扰

Whisper

LinearARTs

exp：

Signin

不完全阻塞干扰

Whisper

LinearARTs

exp：