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1336 - Sigma Function
  PDF (English) Statistics Forum
Time Limit: 2 second(s) Memory Limit: 32 MB

Sigma function is an interesting function in Number Theory. It is denoted by the Greek letter Sigma (σ). This function actually denotes the sum of all divisors of a number. For example σ(24) = 1+2+3+4+6+8+12+24=60. Sigma of small numbers is easy to find but for large numbers it is very difficult to find in a straight forward way. But mathematicians have discovered a formula to find sigma. If the prime power decomposition of an integer is

Then we can write,

For some n the value of σ(n) is odd and for others it is even. Given a value n, you will have to find how many integers from 1 to n have even value of σ.

Input

Input starts with an integer T (≤ 100), denoting the number of test cases.

Each case starts with a line containing an integer n (1 ≤ n ≤ 1012).

Output

For each case, print the case number and the result.

Sample Input

Output for Sample Input

4

3

10

100

1000

Case 1: 1

Case 2: 5

Case 3: 83

Case 4: 947

 


Problem Setter: Shahriar Manzoor
Special Thanks: Jane Alam Jan (Solution, Dataset)
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