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

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

The pedestal consists of 3$3$ platforms for 2$2$-nd, 1$1$-st and 3$3$-rd places respectively. The platform for the 1$1$-st place must be strictly higher 

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than for the 2$2$-nd place, and the platform for the 2$2$-nd place must be strictly higher than for the 3$3$-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$n=11$ blocks: second place height equals 4$4$ blocks, first place height equals 5$5$ blocks, third place height equals 2$2$ blocks.

Among all possible pedestals of n$n$ blocks, deduce one such that the platform height for the 1$1$-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$t$ (1≤t≤104$1\le t\le {10}^4$) — the number of test cases.

Print a Pedestal (Codeforces logo?) Codeforces Solution

Each test case contains a single integer n$n$ (6≤n≤105$6\le n\le {10}^5$) — the total number of blocks for the pedestal. All n$n$ blocks must be used.

It is guaranteed that the sum of n$n$ values over all test cases does not exceed 106${10}^6$.

Output

For each test case, output 3$3$ numbers h2,h1,h3$h_2,h_1,h_3$ — the platform heights for 2$2$-nd, 1$1$-st and 3$3$-rd places on a pedestal consisting of n$n$ blocks (h1+h2+h3=n$h_1+h_2+h_3=n$, 0<h3<h2<h1$0<h_3<h_2<h_1$).

Among all possible pedestals, output the one for which the value of h1$h_1$ minimal. If there are several of them, output any of them.