We all know that any integer number n is divisible by 1 and n. That is why these two numbers are not the actual divisors of any numbers. The function SOD(n) (sum of divisors) is defined as the summation of all the actual divisors of an integer number n. For example, SOD(24) = 2+3+4+6+8+12 = 35.
The function CSOD(n) (cumulative SOD) of aninteger n, is defined as below:
$$CSOD(n) = \sum_{i=1}^nSOD(i)$$
Given the value of n, your job is to find the value of CSOD(n).
Input
Input starts with an integer T (≤ 1000), denoting the number of test cases.
Each case contains an integer n (0 ≤ n ≤ 2 * 109).
Output
For each case, print the case number and the result. You may assume that each output will fit into a 64 bit signed integer.
Sample
| Sample Input | Sample Output |
|---|---|
3 2 100 200000000 | Case 1: 0 Case 2: 3150 Case 3: 12898681201837053 |