Minimum’s Revenge

There is a graph of n vertices which are indexed from 1 to n. For any pair of different vertices, the weight of the edge between them is the least common multiple of their indexes.

Mr. Frog is wondering about the total weight of the minimum spanning tree. Can you help him?

The first line contains only one integer T ($T \leq 100$), which indicates the number of test cases.

For each test case, the first line contains only one integer n ($2 \leq n \leq 10^9$), indicating the number of vertices.

For each test case, output one line "Case #x：y",where x is the case number (starting from 1) and y is the total weight of the minimum spanning tree.

2
2
3

Case #1: 2
Case #2: 5

In the second sample, the graph contains 3 edges which are (1, 2, 2), (1, 3, 3) and (2, 3, 6). Thus the answer is 5.