Problem　　Description

For decades, scientists have wondered whether each of the numbers from 0 to 100 could be represented as the sum of three cubes, where a cube is the same number multiplied together three times.

42 was the last number without a proven solution — until now.

The solution is (−80538738812075974)3+804357581458175153+126021232973356313=42

Now, Yen-Jen is suspicious of the existence of other solutions. But, the solutions are not so trivial to find out.

Yen-Jen wants to find out easysolutions first. That is, for the equation a3+b3+c3=xYen-Jen wants to find out at least one solution for each integer xx in [0,200],where |a|,|b|,|c|≤5000.

Since Yen-Jen is still busy preparing the test data of some(this?) problem, pleasehelp him find out at least one solution for each xx or tell him that thesolution doesn't exist when |a|,|b|,|c|≤5000.

Input

The first line contains an integer TT indicating the number of xx to bechecked.Following TT lines each contains one integer xx.

• 1≤T≤10
  
• 0≤x≤200
  

Output

For each test case, output one line containing three space-separated integers a,b,ca,b,c such that a3+b3+c3=x and |a|,|b|,|c|≤5000. If thesolution doesn't exist, output impossible.

Sample Input

2
1
2

Sample Output

1 1 -1
1 1 0

这道题的答案范围x是0~200。但是需要枚举3个变量a,b,c且每个范围都是-5000~5000.
因此不管是什么方法应该TLE是跑不了（没错这竟然是一道不打表过不了的题（应该吧））
注意5000的3次还需要用到long long。
然后a,b,c三个变量的关系要么3正，要么2正1负要么1正2负。（不过3正好像也可以去掉……因为包含其中了？）
具体代码看这位大佬的吧qwq（里面有unordered_map和文件freopen）