Vali and Munnazzar are playing a game based on number theory. Vali challenges Munnazzar to find three distinct integers a, a, and c such that for a given integer n:

a^n + b^n = c^n

If such integers exist, the program should print a, b, and c. Otherwise, it should output -1.

Input

The first line contains an integer t (1 ≤ t ≤ 100) — the number of test cases.

Each test case contains a single line containing an integer n  (1 ≤ n ≤ 10,000).

Output

For each test case, print 3 distinct integers a, b, and c if they exist; otherwise, print -1.
It is to be noted that 0 < a, b, c.
If there exist multiple answers, print any.

Example

Input:
1
1

Output:
1 2 3