Sums

Given an integer $n$, express it as the sum of at least two consecutive positive integers. For example:

• $10=1+2+3+4$

• $24=7+8+9$

If there are multiple solutions, output the one with the smallest possible number of summands.

Input

The first line contains the number of test cases $t$. Each test case consists of one line containing an integer $n(1\le n\le 10^9)$.

Output

For each test case, output a single line containing the equation in the format:

as in the example. If there is no solution, output a single word IMPOSSIBLE instead.

Examples