import math
from itertools import permutations


def first_n_digits(num, n):
    # https://stackoverflow.com/questions/41271299/how-can-i-get-the-first-two-digits-of-a-number
    p = int(math.log(num, 10)) - n + 1
    if p < 0:
        return num
    return num // 10 ** (int(math.log(num, 10)) - n + 1)


def is_end_pandigital(n, ps):
    return (n % 10**9) in ps


def is_start_pandigital(n, ps):
    start = first_n_digits(n, 9)
    return start in ps


def euler_104():
    a, b = 1, 1
    ps = set([int("".join(map(str, p))) for p in permutations(range(1, 10))])
    k = 3
    while True:
        a, b = b, a + b
        if is_end_pandigital(b, ps) and is_start_pandigital(b, ps):
            return k
        k += 1


if __name__ == "__main__":
    solution = euler_104()
    print("e104.py: " + str(solution))
    assert(solution == 329468)