Number Theory?

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)

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Description

In number theory, for a positive number N, two properties are often mentioned, one is Euler's function, short for E(N), another is factor number, short for F(N).
To be more precise for newbie, here we recall the definition of E(N) and F(N) again.
E(N) = |{i | gcd(N, i) = 1, 1 <= i <= N}|
F(N) = |{i | N % i = 0, 1 <= i <= N}|
Here |Set| indicates the different elements in the Set.
As a number fanaticism, iSea want to solve a simple problem now. Given a integer N, try to find the number of intervals [l, r], l is no bigger than r obviously, strictly fit in the interval [1, N]. It's a piece of cake for clever you, of course. But here he also has another troublesome restrict:

Input

The first line contains a single integer T, indicating the number of test cases. Each test case includes one integer N.

Technical Specification
1. 1 <= T <= 1 000
2. 1 <= N <= 1 000 000 000

Output

For each test case, output the case number first, then the number of intervals.

Sample Input

2 2 9

Sample Output

Case 1: 1 Case 2: 6

Hint

lcy

Source

首届华中区程序设计邀请赛暨第十届武汉大学程序设计大赛

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