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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
4
3
10
100
1000
Sample Output
Case 1: 1
Case 2: 5
Case 3: 83

Case 4: 947

https://blog.csdn.net/strangedbly/article/details/50908522

#include<map>
#include<stack>
#include<queue>
#include<math.h>
#include<vector>
#include<string>
#include<stdio.h>
#include<iostream>
#include<string.h>
#include<algorithm>
#define mem(a,b) memset(a,b,sizeof(a))
#define maxn 1100000
#define maxm 1000000000005
#define mod 1000000007
#define ll long long
#define inf 0x3f3f3f3f
using namespace std;
int main(){
    int t,test=0;scanf("%d",&t);
    while(t--){
        ll n;scanf("%lld",&n);
        ll ans=0;
        ans=(ll)sqrt(n*1.0);
        ans+=(ll)sqrt(n/2.0);
        printf("Case %d: %lld
",++test,n-ans);
    }
}