You are given a non-negative integer N. Your task is to return the largest exponent e such that 2e divides N! (N factorial).
To find this exponent efficiently, count the number of factors of 2 contributed by all multiples of 2, 4, 8, and higher powers of 2 that do not exceed N. Add these counts to obtain the final result.
Input: N = 10
Output: 8
Explanation: The exponent is calculated as 10 / 2 + 10 / 4 + 10 / 8 = 5 + 2 + 1 = 8.
Input: N = 5
Output: 3
Explanation: The exponent is calculated as 5 / 2 + 5 / 4 = 2 + 1 = 3.
Input: N = 1
Output: 0
Explanation: 1! = 1 is not divisible by 2, so the largest possible exponent is 0.
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