class ComComplex:
    def __init__(self, value=[0,0,0,0]):
        self.value = value
    def __str__(self):
        s = str(self.value[0])
        for k,i in enumerate(self.value[1:]):
            if i >= 0:
                s += '+'
            s += str(i) +'ijk'[k]
        return s
    def __add__(self,x):
        return ComComplex([i+j for i,j in zip(self.value,x.value)])
    def __mul__(self,x):
        a = self.value[0]*x.value[0]-self.value[1]*x.value[1]-self.value[2]*x.value[2]-self.value[3]*x.value[3]
        b = self.value[0]*x.value[1]+self.value[1]*x.value[0]+self.value[2]*x.value[3]-self.value[3]*x.value[2]
        c = self.value[0]*x.value[2]-self.value[1]*x.value[3]+self.value[2]*x.value[0]+self.value[3]*x.value[1]
        d = self.value[0]*x.value[3]+self.value[1]*x.value[2]-self.value[2]*x.value[1]+self.value[3]*x.value[0]
        return ComComplex([a,b,c,d])
    def __mod__(self,x):
        return ComComplex([i % x for i in self.value])
    def __pow__(self, x, n=None):
        tmp = ComComplex(self.value)
        a = ComComplex([1,0,0,0])
        while x:
            if x & 1:
                a *= tmp
            tmp *= tmp
            if n:
                a %= n
                tmp %= n
            x >>= 1
        return a

from Crypto.Util.number import *
from secret import flag, hint

p = getPrime(256)
q = getPrime(256)
r = getPrime(256)
n = p * q * r

P = getPrime(512)
assert len(hint) == 20
hints = ComComplex([bytes_to_long(hint[i:i+5]) for i in range(0,20,5)])
keys = ComComplex([0, p, q, r])
print('hint =',hints)
print('gift =',hints*keys%P)
print('P =',P)

e = 65547
m = ComComplex([bytes_to_long(flag[i:i+len(flag)//4+1]) for i in range(0,len(flag),len(flag)//4+1)])
c = pow(m, e, n)
print('n =', n)
print('c =', c)

'''
hint = 375413371936+452903063925i+418564633198j+452841062207k
gift = 8123312244520119413231609191866976836916616973013918670932199631084038015924368317077919454611785179950870055560079987034735836668109705445946887481003729+20508867471664499348708768798854433383217801696267611753941328714877299161068885700412171i+22802458968832151777449744120185122420871929971817937643641589637402679927558503881707868j+40224499597522456323122179021760594618350780974297095023316834212332206526399536884102863k
P = 8123312244520119413231609191866976836916616973013918670932199631182724263362174895104545305364960781233690810077210539091362134310623408173268475389315109
n = 408713495380933615345467409596399184629824932933932227692519320046890365817329617301604051766392980053993030281090124694858194866782889226223493799859404283664530068697313752856923001112586828837146686963124061670340088332769524367
c = 212391106108596254648968182832931369624606731443797421732310126161911908195602305474921714075911012622738456373731638115041135121458776339519085497285769160263024788009541257401354037620169924991531279387552806754098200127027800103+24398526281840329222660628769015610312084745844610670698920371305353888694519135578269023873988641161449924124665731242993290561874625654977013162008430854786349580090169988458393820787665342793716311005178101342140536536153873825i+45426319565874516841189981758358042952736832934179778483602503215353130229731883231784466068253520728052302138781204883495827539943655851877172681021818282251414044916889460602783324944030929987991059211909160860125047647337380125j+96704582331728201332157222706704482771142627223521415975953255983058954606417974983056516338287792260492498273014507582247155218239742778886055575426154960475637748339582574453542182586573424942835640846567809581805953259331957385k
'''