Project Euler #21: Amicable numbers

_{This problem is a programming version of Problem 21 from projecteuler.net}

Let be defined as the sum of proper divisors of (numbers less than which divide evenly into ).
If and , where , then and are an amicable pair and each of and are called amicable numbers.

For example, the proper divisors of are therefore . The proper divisors of are so .

Evaluate the sum of all the amicable numbers under .

Input Format

The first line contains an integer , i.e., number of test cases.
Next lines will contain an integer .

Constraints

Output Format

Print the values corresponding to each test case.

Sample Input

1
300

Sample Output

Explanation

Under we only have and , sum is