Description

gaelookair is searching for his pair everywhere. why? gaelookair = ge + look + pair. Isn't it? Happy Christmas everyone! A simple problem is given for you (Acmers).

Given a non-negitive number n, you should find out pair(a, b) which is satisfied the rules below:

    1. a * b = n.

    2. a < b < 2 ^ 30.

    3. a, b, n are all non-negitive.

You just need output the number of the pairs. Simple? Really?

Input

The first line is an integer T, indicates the number of cases. Then follow T cases(T <= 100). The first line of each case has one non-negitive integer n (n < 2^30), which has describled above.

Output

For each case, you should output the number of pairs which meet(s) the conditions describled above in one line.

Sample

Input

3
1 2 3

Output

0
1
1

Hint

n == 1, none meets the condition. n == 2, only (1, 2) meets the condition. n == 3, only (1, 3) meets the condition.

Source: polym