"""
We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once;
for example, the 5-digit number, 15234, is 1 through 5 pandigital.

The product 7254 is unusual, as the identity, 39 × 186 = 7254,
containing multiplicand, multiplier, and product is 1 through 9 pandigital.


Find the sum of all products whose multiplicand/multiplier/product identity can be written
as a 1 through 9 pandigital.
HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.
"""

import time
from itertools import permutations


def timer(func):
    def wrapper(*args, **kwargs):
        start = time.time()
        result = func(*args, **kwargs)
        end = time.time()
        print(f"{func.__name__} took {end - start:.6f} seconds")
        return result

    return wrapper


def is_pandigital(n: list[str]) -> bool:
    if n[0] == "1":
        x = [int("".join(n[:2]))]
        y = [int("".join(n[2:5]))]
    else:
        x = [int(n[0]), int("".join(n[:2]))]
        y = [int("".join(n[1:5])), int("".join(n[2:5]))]
    z = int("".join(n[5:]))
    for i in range(len(x)):
        if x[i] * y[i] == z:
            return True
    return False


def pandigital_products() -> list[int]:
    all_permuts = permutations("123456789")
    res = set()
    for perm in all_permuts:
        if is_pandigital(list(perm)):
            res.add(int("".join(perm[5:])))
    return list(res)


@timer
def main_compute() -> None:
    res = set()
    for x in range(2, 10):
        for z in range(1234, 9877):
            if z % x == 0:
                y = z // x
                if "".join(sorted(str(x) + str(y) + str(z))) == "123456789":
                    res.add(z)
                    print(f"{x} * {y} = {z}")
    for x in range(12, 99):
        for z in range(1234, 9877):
            if z % x == 0:
                y = z // x
                if "".join(sorted(str(x) + str(y) + str(z))) == "123456789":
                    res.add(z)
                    print(f"{x} * {y} = {z}")
    res = list(res)
    print(f"= {sum(res)}")


@timer
def main() -> None:
    res = pandigital_products()
    print("+".join(map(str, res)))
    print(f"= {sum(res)}")


if __name__ == "__main__":
    main()
    main_compute()