Mino

#!/usr/bin/env python3

import sys
from flag import flag

def die(*args):
    pr(*args)
    quit()

def pr(*args):
    s = " ".join(map(str, args))
    sys.stdout.write(s + "\n")
    sys.stdout.flush()

def sc():
    return sys.stdin.readline().strip()

def main():
    border = "|"
    pr(border*72)
    pr(border, "Hi crypto programmers! I'm looking for some very special permutation", border)
    pr(border, "p name MINO such that sum(p(i) * (-2)^i) = 0 from 0 to n - 1, for   ", border)
    pr(border, "example for n = 6, the permutation p = (4, 2, 6, 5, 3, 1) is MINO:  ", border)
    pr(border, "4*(-2)^0 + 2*(-2)^1 + 6*(-2)^2 + 5*(-2)^3 + 3*(-2)^4 + 1*(-2)^5 = 0 ", border)
    pr(border, "In each step find such permutation and send to server, if there is  ", border)
    pr(border, "NOT such permutation for given n, just send `TINP', good luck :)    ", border)
    pr(border*72)
    step, final = 3, 40
    while True:
        pr(border, f"Send a MINO permutation of length = {step} separated by comma: ")
        p = sc().split(',')
        if step % 3 == 1:
            if p == ['TINP']:
                if step == final: die(border, f"Congrats, you got the flag: {flag}")
                else:
                    pr(border, "Great, try the next level :)")
                    step += 1
            else:
                die(border, "the answer is not correct, bye!!!")
        elif len(p) == step:
            try:
                p = [int(_) for _ in p]
            except:
                pr(border, "the permutation is not valid")
            if set(p) == set([_ for _ in range(1, step + 1)]):
                S = 0
                for _ in range(step):
                    S += p[_] * (-2) ** _
                if S == 0:
                    if step == final: 
                        die(border, f"Congrats, you got the flag: {flag}")
                    else:
                        pr(border, "Great, try the next level :)")
                        step += 1
                else:
                    die(border, "the answer is not correct, bye!!!")
            else:
                pr(border, "the permutation is not valid!!!")
        else:
            die(border, f"the length of permutation is not equal to {step}")

if __name__ == "__main__":
    main()

for n in (3,5,6,8):
    print("=== LENGTH", n, "===")
    G = SymmetricGroup(n)
    c = 0
    for g in G:
        t = g.tuple()
        if sum(t[i] * (-2)**i for i in range(n)) == 0:
            print(t)
            c += 1

def sum_(t):
    return sum(t[i] * pow(-2, i) for i in range(len(t)))

def children(t):
    n = len(t)
    if n % 3 == 2:
        k = (n+1)//3
        for i in range(n):
            if sum_(t[-i:]) == k:
                child = t[:-i] + [3*k] + t[-i:]
                assert sum_(child) == 0
                yield child
    else:
       k = n//3
       for i in range(n):
           if sum_(t[-i:]) == k:
               child = t[:-i] + [3*k+2, 3*k+1] + t[-i:]
               assert sum_(child) == 0
               yield child
           elif sum_(t[-i:]) == k + 1:
               child = t[:-i] + [3*k+1, 3*k+2] + t[-i:]
               assert sum_(child) == 0
               yield child

p = [2, 3, 1]
assert sum_(p) == 0
print(",".join(str(n) for n in p))
print("TINP")
for i in range(40):
    p = next(children(p))
    print(",".join(str(n) for n in p))
    if len(p) % 3 == 0:
        print("TINP") # for len(p)+1
    if len(p) == 39:
        break