Sum of Consecutive Natural Numbers

Time limit1sMemory limit128 MB

Problem

Given a natural number N, count how many ways it can be written as the sum of at least two consecutive natural numbers.

Two representations are different if they start with a different natural number or use a different number of terms. Every term must be a positive integer, and adjacent terms must differ by 1.

Input

The first line contains the number of test cases T.

Each of the next T lines contains one natural number N. Every N is less than 2^31.

Output

For each test case, print one line containing the number of ways to write N as the sum of at least two consecutive natural numbers.