Description

Given the integer $n$ — the number of available blocks. You must use all blocks to build a pedestal.

The pedestal consists of $3$ platforms for $2$-nd, $1$-st and $3$-rd places respectively. The platform for the $1$-st place must be strictly higher than for the $2$-nd place, and the platform for the $2$-nd place must be strictly higher than for the $3$-rd place. Also, the height of each platform must be greater than zero (that is, each platform must contain at least one block).

Example pedestal of $n=11$ blocks: second place height equals $4$ blocks, first place height equals $5$ blocks, third place height equals $2$ blocks.

Among all possible pedestals of $n$ blocks, deduce one such that the platform height for the $1$-st place minimum as possible. If there are several of them, output any of them.

Input

The first line of input data contains an integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

Each test case contains a single integer $n$ ($6 \le n \le 10^5$) — the total number of blocks for the pedestal. All $n$ blocks must be used.

It is guaranteed that the sum of $n$ values over all test cases does not exceed $10^6$.

Output

For each test case, output $3$ numbers $h_2, h_1, h_3$ — the platform heights for $2$-nd, $1$-st and $3$-rd places on a pedestal consisting of $n$ blocks ($h_1+h_2+h_3=n$, $0 < h_3 < h_2 < h_1$).

Among all possible pedestals, output the one for which the value of $h_1$ minimal. If there are several of them, output any of them.

6
11
6
10
100000
7
8
 
 
 

4 5 2
2 3 1
4 5 1
33334 33335 33331
2 4 1
3 4 1

Note

In the first test case we can not get the height of the platform for the first place less than $5$, because if the height of the platform for the first place is not more than $4$, then we can use at most $4 + 3 + 2 = 9$ blocks. And we should use $11 = 4 + 5 + 2$ blocks. Therefore, the answer 4 5 2 fits.

In the second set, the only suitable answer is: 2 3 1.