Calculate the number of ordered triples of positive integers (a, b, c) such that their multiple abc is not larger than a given integer N (1 <= N <= 10¹¹).

Input

Each test case contains a single line - N. Input terminates by EOF.

Output

For each test case output its case number (starting from 1) and the answer in a single line.

Example

Input:
1
3
6
10
15
21
28
Output:
Case 1: 1
Case 2: 7
Case 3: 25
Case 4: 53
Case 5: 95
Case 6: 161
Case 7: 246