Problem:
Score : 400 points

Problem Statement

We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.

You are given Q queries.

In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x similar to 2017 such that l_i ≤ x ≤ r_i.

Constraints

1≤Q≤10^5

1≤l_i≤r_i≤10^5

l_i and r_i are odd.

All input values are integers.

Input

Input is given from Standard Input in the following format:

Q
l_1 r_1
:
l_Q r_Q

Output

Print Q lines. The i-th line (1≤i≤Q) should contain the response to the i-th query.

Sample Input 1

1
3 7

Sample Output 1

2

3 is similar to 2017, since both 3 and (3+1)/2=2 are prime.

5 is similar to 2017, since both 5 and (5+1)/2=3 are prime.

7 is not similar to 2017, since (7+1)/2=4 is not prime, although 7 is prime.

Thus, the response to the first query should be 2.

Sample Input 2

4
13 13
7 11
7 11
2017 2017

Sample Output 2

1
0
0
1

Note that 2017 is also similar to 2017.

Sample Input 3

6
1 53
13 91
37 55
19 51
73 91
13 49

Sample Output 3

4
4
1
1
1
2

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <cmath>
#include <vector>

using namespace std;

bool sosuu(int N){
    bool flag = true;

    for (int i = 2; i * i <= N; i++){
        if (N % i == 0){
            flag = false;
        }
    }
    
    return flag;

}

int main(){

    vector <int> like;

    for (int i = 3; i < 100000; i++){
        if (sosuu(i) == true && sosuu((i + 1) / 2) == true){
            like.push_back(i);
        }
    }

    vector <int> search(100001);
    int j = 0;
    for (int i = 1; i < 100001; i++){
        search[i] = search[i - 1];
        if (i >= like[j]){
            search[i]++;
            j++;
        }
    }
    

    int Q;
    cin >> Q;

    vector <int> ans(Q);

    for (int i = 0; i < Q; i++){
        int l, r;
        cin >> l >> r;

        ans[i] = search[r] - search[l - 1];
    }

    for (int i = 0; i < Q; i++){
        cout << ans[i] << endl;
    }
        
    
    return 0;
}