2^x mod n = 1

Give a number n, find the minimum x that satisfies 2^x mod n = 1.

Input

One positive integer on each line, the value of n.

Output

If the minimum x exists, print a line with 2^x mod n = 1.

Print 2^? mod n = 1 otherwise.

You should replace x and n with specific numbers.

Sample Input

2
5

Sample Output

2^? mod 2 = 1
2^4 mod 5 = 1

http://blog.csdn.net/wmn_wmn/article/details/7371607

http://www.cnblogs.com/cszlg/p/3277135.html