Description

This problem is a programming version of Problem 21 from projecteuler.net
Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers.
For example, the proper divisors of 220 are 1,2,4,5,10,11,20,22,44,55 and 110 therefore d(220) = 284. The proper divisors of 284 are 1,2,4,71 and 142 so d(284) = 220.
Evaluate the sum of all the amicable numbers under N.
Input Format
The first line contains an integer T , i.e., number of test cases.
Next T lines will contain an integer N.
Output Format
Print the values corresponding to each test case.
Constraints
1 ≤ T ≤ 1000
1 ≤ N ≤ 105
Sample Input

Sample Output