Given natural number N you have to find a right triangle let the lengths of its sides are a, b, c.

This right triangle must satisfy:

• a, b, c are positive integers.
• a < b < c.
• c - b = 1.
• a = N.

Input

The first fine of input file has one integer T (1 <= T <= 10⁵) the number of test cases.

T lines follow, each consisting of one integer N (1 <= N <= 10⁹)

Output

if there is such right triangle then output its side lengths a, b, c respectively otherwise output -1.

Example

Input:
3
3
4
5

Output:
3 4 5
-1
5 12 13