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ZOJ Problem Set - 1489
2^x mod n = 1

Time Limit: 2 Seconds      Memory Limit: 65536 KB

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



Author: MA, Xiao
Source: ZOJ Monthly, February 2003
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