2^x mod n = 1

Time Limit: Java: 2000 ms / Others: 2000 ms

Memory Limit: Java: 65536 KB / Others: 65536 KB

Description

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

Hint

None

Source

ZOJ Monthly, February 2003

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