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 $$(-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3 = 42$$

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 easy solutions first. That is, for the equation $a^3 + b^3 + c^3 = x$, Yen-Jen wants to find out at least one solution for each integer $x$ in $[0, 200]$, where $|a|, |b|, |c| \le 5000$.

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

Input

The first line contains an integer $T$ indicating the number of $x$ to be checked.

Following $T$ lines each contains one integer $x$.

• $1 \le T \le 10$
• $0 \le x \le 200$

Output

For each test case, output one line containing three space-separated integers $a, b, c$ such that $a^3 + b^3 + c^3 = x$ and $|a|, |b|, |c| \le 5000$. If the solution doesn't exist, output $\texttt{"impossible"}$.

Sample Input

2
1
2

Sample Output

1 1 -1
1 1 0