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1375 - LCM Extreme
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Time Limit: 4 second(s) Memory Limit: 64 MB

Find the result of the following code:

unsigned long long allPairLcm( int n ) {
    
unsigned long long res = 0;
    
for( int i = 1; i <= n; i++ )
        
for( int j = i + 1; j <= n; j++ )
            res 
+= lcm(i, j); // lcm means least common multiple
    
return res;
}

A straight forward implementation of the code may time out.

Input

Input starts with an integer T (≤ 2*105), denoting the number of test cases.

Each case starts with a line containing an integer n (1 ≤ n ≤ 3*106).

Output

For each case, print the value returned by the function 'allPairLcm(n)'. As the result can be large, we want the result modulo 264.

Sample Input

Output for Sample Input

4

2

10

13

100000

Case 1: 2

Case 2: 1036

Case 3: 3111

Case 4: 9134672774499923824

Note

Dataset is huge, use faster I/O Methods.


Problem Setter: Jane Alam Jan
Special Thanks: Derek Kisman, Tasnim Imran Sunny
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