Write trailing_zeros(n) that returns how many zeros n! (n factorial) ends with. For example 10! = 3628800 ends with two zeros.
Do not build the factorial itself: for the largest inputs it would have hundreds of millions of digits.
Examples
Input: n = 5
Output: 1
Input: n = 10
Output: 2
Input: n = 25
Output: 6
Constraints
0 <= n <= 10**9
Goals
- Reason about where trailing zeros come from
- Avoid computing a huge factorial at all