3.3 Friends for factorization

Score: 80pts

Time Limit: 3.00 sec

You are in the middle of the most boring lecture of your course (Not PCE).

You are least interested and want to do something challenging.

Your friend too , is not interested in the lecture. However he has invented a math problem ,just for fun. He takes a random number N and finds the sum of pairwise product of all its divisors. You find it very weird.

So for eg : the number is 4 , it has 3 divisors {1 , 2 , 4}

The sum of pairwise product of divisors : (1*2)+(1*4)+(2*4) = 14

Similarly for 10 it will be : (1*2)+(1*5)+(1*10)+(2*5)+(2*10)+(5*10) = 97

Now your friend challenges you to write a code for solving this problem.

You were smiling from inside , because this is what you wanted.

So your friend gives you T integers and you need to calculate the summation of the pairwise product of divisors of each number.

You are least interested and want to do something challenging.

Your friend too , is not interested in the lecture. However he has invented a math problem ,just for fun. He takes a random number N and finds the sum of pairwise product of all its divisors. You find it very weird.

So for eg : the number is 4 , it has 3 divisors {1 , 2 , 4}

The sum of pairwise product of divisors : (1*2)+(1*4)+(2*4) = 14

Similarly for 10 it will be : (1*2)+(1*5)+(1*10)+(2*5)+(2*10)+(5*10) = 97

Now your friend challenges you to write a code for solving this problem.

You were smiling from inside , because this is what you wanted.

So your friend gives you T integers and you need to calculate the summation of the pairwise product of divisors of each number.

Constraints

1 <= T <= 102

1 <= N <= 105

Sum of N over all the test cases does not exceed 105.

1 <= N <= 105

Sum of N over all the test cases does not exceed 105.

Input Format

First line: denoting the test cases T

Next T lines containing a single integer

Next T lines containing a single integer

Output Format

Single integer representing the answer.

Example 1

Input:

2

4

10

Output:

14

97

Explanation:

In the first test case ,

The number is 4 , it has 3 divisors {1 , 2 , 4}

The sum of pairwise product of divisors : (1*2)+(1*4)+(2*4) = 14

2

4

10

Output:

14

97

Explanation:

In the first test case ,

The number is 4 , it has 3 divisors {1 , 2 , 4}

The sum of pairwise product of divisors : (1*2)+(1*4)+(2*4) = 14