After Problem 2319 and 2320.

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 ([391867254]).

Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through n pandigital (n is given in input).

HINT1: Some products can be obtained in more than one way so be sure to only include it once in your sum.

HINT2: All in good time...