Description

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 Format

The first line of input contains the number of test cases $T$. The descriptions of the test cases follow:

Each test case consists of one line containing an integer $N(1 \le N \le 10^9)$.

Output Format

For each test case, output a single line containing the equation in the format: N = a + (a+1) + ... + b as in the example. If there is no solution, output a single word IMPOSSIBLE instead.

3
8
10
24

IMPOSSIBLE
10 = 1 + 2 + 3 + 4
24 = 7 + 8 + 9