A Simple Problem

For a given positive integer n, please find the smallest positive integer x that we can find an integer y such that

y^2 = n + x^2.

Input

The first line is an integer T, which is the the number of cases. Then T line followed each containing an integer n (1 ≤ n ≤ 10^9).

Output

For each integer n, please print output the x in a single line, if x does not exit , print -1 instead.

Examples