Count Divisors (Extreme)

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Points: 15
Time limit: 1.0s
Memory limit: 64M

Problem type

Given a positive integer \(N\) please determine the number of unique divisors of \(N\).

An integer \(X\) is a divisor of \(N\) if there exists an integer \(K\) where \(X \cdot K = N\).

Note: The constraints are updated in this problem. For C++ and Java users please make sure to use 64-bit integers to store the input without overflow.

Input Specification

The first line of the input will contain an integer \(N\) \((1 \le N \le 10^{18})\).

Output Specification

Output an integer representing the number of unique divisors of \(N\).

Sample Input


Sample Output


Sample Explanation

The divisors of \(9\) are \(1\), \(3\), and \(9\).