Competitions

# Factorization.

# 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** ≤ **n** ≤ `10`

).^{9}

#### 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.

Input example #1

3 8 10 24

Output example #1

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