```from sage.all import factorfrom pwn import remote
r = remote("challs.xmas.htsp.ro", 6050)r.recvuntil("1/100")
for i in range(100):    print(i)    r.recvuntil("gcd(x, y) = ")    g = int(r.recvuntil("\n").strip())    r.recvuntil("lcm(x, y) = ")    l = int(r.recvuntil("\n").strip())    if g==l:        r.sendline("1")    else:        _g = list(factor(g))        _l = list(factor(l))        #print(_g)        #print(_l)        count = 0        for f in _l:            if f not in _g:                count += 1        r.sendline(str(2**count))    print(r.recvuntil("\n")) print(r.recvuntil("\n"))print(r.recvuntil("\n"))```