2^x mod n = 1

Time Limit: 1 Second    Memory Limit: 32768 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

Submit

Source: ZOJ Monthly, February 2003