A user inputs a long positive number m. You need to find out what is the smallest int number n such that n! > m.
n!, or factorial n, is a product of all natural numbers from 1 to n inclusive: for example, 5! = 1 * 2 * 3 * 4 * 5.
Just in case: wiki on factorials.
For example, the user enters 100. This means m = 100 and n = 5 because 5! = 120 (see the factorial formula) and this is the smallest number that satisfies the condition n! > m.
Pay attention that the user may input a really big number so choose an appropriate data type!