Competitions

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 (1n109).

Output

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.

Time limit 1 second
Memory limit 128 MiB
Input example #1
3
8
10
24

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

Source 2014 ACM Central Europe (CERC), Problem C