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Tavrida NU Akai contest. Petrozavodsk training camp. Summer 2010

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D. Random Shuffler

Time limit: 0.5 second
Memory limit: 64 MB
Once Sasha decided that a random shuffler in his favourite media player should be replaced. Sasha wants to calculate the order of songs according to the following rule:
x0 = 0,
xi = (xi − 1 · a + b) mod m,
where m is the total number of songs, a and b are integers in range from 0 to m − 1. Generated sequence of song numbers should satisfy the following rules:
  • x0xm − 1 should be a permutation of integers from 0 to m − 1,
  • xm should be equal to zero.
Sasha wants to find all pairs (ai, bi), resulting in a valid sequences and calculate the average among all ai. Help him do it.

Input

The input consists of at most 100 test cases. Each test case is a single line containing an integer m (1 < m < 109).

Output

For each test case output in a single line the average among ai, rounded down.

Sample

inputoutput
2
36
100
123
1
13
41
1
Problem Source: Tavrida NU Akai Contest. Petrozavodsk Summer Session, August 2010.
To submit the solution for this problem go to the Problem set: 1813. Random Shuffler