Frankfurt UAS, KMITL, VGU & SPbGUT - Combinatorics & Number Theory

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2017-03-26 21:00 AKDT

Frankfurt UAS, KMITL, VGU & SPbGUT - Combinatorics & Number Theory

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2017-03-30 10:00 AKDT
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Problem U
A List Game

/problems/listgame/file/statement/en/img-0001.jpg
Picture in public domain via Wikimedia Commons

You are playing the following simple game with a friend:

  1. The first player picks a positive integer $X$.

  2. The second player gives a list of $k$ positive integers $Y_1, \ldots , Y_ k$ such that $(Y_1+1)(Y_2+1) \cdots (Y_ k+1) = X$, and gets $k$ points.

Write a program that plays the second player.

Input

The input consists of a single integer $X$ satisfying $10^3 \le X \le 10^9$, giving the number picked by the first player.

Output

Write a single integer $k$, giving the number of points obtained by the second player, assuming she plays as good as possible.

Sample Input 1 Sample Output 1
65536
16
Sample Input 2 Sample Output 2
127381
3