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 answer always exists.

Note

In the first test case, $6 + 9 + 3 = 18$ and $\operatorname{gcd}(6, 9) = 3$.

In the second test case, $21 + 39 + 3 = 63$ and $\operatorname{gcd}(21, 39) = 3$.

In the third test case, $29 + 43 + 1 = 73$ and $\operatorname{gcd}(29, 43) = 1$.

Samples

6
18
63
73
91
438
122690412

6 9 3
21 39 3
29 43 1
49 35 7
146 219 73
28622 122661788 2