How Many Pairs of LCM?

A Common Multiple of two integers a and b is an integer X, such that both a and b divides X. A number is called Least Common Multiple of a pair (a,b) if it is the smallest among all possible values of X.

Given X, you will have to count how many pairs of integers are there where LCM(a,b)=X.

Input

The only line of input contains a positive integer X (<=1000000).

For 50 points, X is not more than 1000.

For 50 points, X is not more than 1000000.

Output

Output a single number as mentioned in the problem.

Samples

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