For every given number n we define x(n) as distance from n to the first number after n in form of 99...99. For example x(100)=899, x(45)=54, etc. Given several n numbers you have to find the Z_p, where x(n) ≡ n (mod p).

Input

First line of input contains one number T (T < 20) - the number of test cases. In each of the next T lines contains one number each to represent n (0 < n < 30000000).

Output

In each line you have to write one number - the least p > 1 that x(n) ≡ n (mod p). If there is no such p the line should contain -1.

Example

Input:
2
234
5

Output:
3
-1

Explanation

x(234)=765. 765 mod 3=0, 234 mod 3=0 => 765 ≡ 234 (mod 3)