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## [Solution] Print a Pedestal (Codeforces logo?) Codeforces Solution

A. Print a Pedestal (Codeforces logo?)
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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.