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Given a positive integer $$$n$$$. Find three distinct positive integers $$$a$$$, $$$b$$$, $$$c$$$ such that $$$a + b + c = n$$$ and $$$\operatorname{gcd}(a, b) = c$$$, where $$$\operatorname{gcd}(x, y)$$$ denotes the greatest common divisor (GCD) of integers $$$x$$$ and $$$y$$$.

Input

The input consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^5$$$) — the number of test cases. Description of the test cases follows.

The first and only line of each test case contains a single integer $$$n$$$ ($$$10 \le n \le 10^9$$$).

Output

For each test case, output three distinct positive integers $$$a$$$, $$$b$$$, $$$c$$$ satisfying the requirements. If there are multiple solutions, you can print any. We can show that an answ

GCD Problem

Examples