Given a non-negative integer n, return the number of trailing zeros in n factorial (n!). For example, 10 factorial equals 3628800 which has 2 trailing zeros. Trailing zeros come from pairs of factors 2 and 5, and since there are always more factors of 2 than factors of 5 in a factorial, you only need to count the factors of 5. Return null for null input. Return 0 for negative inputs.
Examples:
Input: n = 0
Output: 0
Explanation: 0 factorial is 1, which has no trailing zeros
Input: n = 5
Output: 1
Explanation: 5 factorial is 120, which has 1 trailing zero
Input: n = 10
Output: 2
Explanation: 10 factorial is 3628800, which has 2 trailing zeros
Input: n = 25
Output: 6
Explanation: Counting factors of 5: 25/5 + 25/25 = 5 + 1 = 6
Input: n = null
Output: null
Explanation: Null input returns null
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