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Eddy's 洗牌问题

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 6952 Accepted Submission(s): 4396

Problem Description

Eddy是个ACMer,他不仅喜欢做ACM题,而且对于纸牌也有一定的研究,他在无聊时研究发现,如果他有2N张牌，编号为1,2,3..n,n+1,..2n。这也是最初的牌的顺序。通过一次洗牌可以把牌的序列变为n+1,1,n+2,2,n+3,3,n+4,4..2n,n。那么可以证明，对于任意自然数N，都可以在经过M次洗牌后第一次重新得到初始的顺序。编程对于小于100000的自然数N，求出M的值。

Input

每行一个整数N

Output

输出与之对应的M

Sample Input

20
1

Sample Output

20
2

Author

Eddy

Source

杭电ACM省赛集训队选拔赛之热身赛

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