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 (1 ≤ t ≤ 50). The descriptions of the test cases follow:

Each test case consists of one line containing an integer n (1 ≤ n ≤ 109).

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.