Euler Totient Sum and Divisors
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  Difficulty: Basic   Marks: 1

The Euler Totient Function for a positive integer N is defined as the number of positive integers less than or equal to N and relatively prime to N.

For example, an algorithm to find Euler Totient Function value of N will be:

int phi(unsigned int N)
{
unsigned int result = 1;
for (int i=2; i < N; i++)
if (gcd(i, N) == 1)
result++;
return result;
}

The task is to find the sum of the Euler Totient Values of all the divisors of the given number.

Input:
The first line of input contains a single integer T denoting the number of test cases. Then T test cases follow. Each test case consists of a single line containing a positive integer N.

Output:
Corresponding to each test case, in a new line, print the sum of the Euler Totient Function values of all the divisors of the given number.


Constraints:
1 ≤ T ≤ 10000
1 ≤ N ≤ 1000000

Example:
Input
2
1
2

Output
1
2

 

** For More Input/Output Examples Use 'Expected Output' option **

Author: Hemang Sarkar


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