Given an integer N, you have to find the number of ways you can express N as sum of consecutive integers. You have to use at least two integers.

For example, N = 15 has three solutions, (1+2+3+4+5), (4+5+6), (7+8).

Input starts with an integer T (≤ 200), denoting the number of test cases.

Each case starts with a line containing an integer N (1 ≤ N ≤ 10¹⁴).

For each case, print the case number and the number of ways to express N as sum of consecutive integers.