"""

The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property.
Let d1 be the 1st digit, d2 be the 2nd digit, and so on. In this way, we note the following:
d2d3d4=406 is divisible by 2
d3d4d5=063 is divisible by 3
d4d5d6=635 is divisible by 5
d5d6d7=357 is divisible by 7
d6d7d8=572 is divisible by 11
d7d8d9=728 is divisible by 13
d8d9d10=289 is divisible by 17
Find the sum of all 0 to 9 pandigital numbers with this property.

"""

import itertools


def has_property(n):
    s = str(n)
    dens = [2, 3, 5, 7, 11, 13, 17]

    for idx, i in enumerate(range(1, 8)):
        num = int(s[i:i+3])
        if num % dens[idx] != 0:
            return False
    return True

digits = (str(i) for i in range(10))
perms = (i for i in itertools.permutations(digits))
nums = (int(''.join(perm)) for perm in perms)
print(sum(i for i in nums if has_property(i)))
