Description

Give a number n, find the minimum x(x>0) 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

Source

ZOJ Monthly, February 2003