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 <iomanip>
#include <cmath>
#include <string>
#include <vector>
#include <cstdlib>
#include <map>
#include <queue>
#include <deque>
#include <algorithm>
#include <stack>
#include <functional>
#include <sstream>
#define rep(i,j,n) for(i=j;i<(n);i++)
#define rrep(i,j,n) for(i=j;i>(n);i--)
typedef long long int lli;
#define N 1000000007
#define M 998244353

using namespace std;

struct like2017{
    lli i,j;
    lli cnt=0;
    vector<lli> vec;
    
    like2017(lli n){
        rep(i,0,n+1){
            if(i%2==0){
                vec.push_back(0);
            }
            else{
                vec.push_back(1);
            }
        }
    }
    
    void check(lli n){
        vec[1]=0;
        vec[2]=1;
        rep(i,1,100001){
            if(vec[i]>=1){
                rep(j,2,100000/i){
                    vec[i*j]=0;
                }
                if(vec[(i+1)/2]>=1){
                    vec[i]=2;
                }
            }
        }
        rep(i,1,100001){
            if(vec[i]==2){
                cnt++;
            }
            vec[i]=cnt;
        }
    }
    
    lli search(lli a,lli b){
        return vec[b]-vec[a-1];
    }
    
};

int main() {
    lli q,l,r;
    vector<lli> ans;
    lli i,j,k;
    cin>>q;
    like2017 num(100000);
    num.check(1);
    rep(i,0,q){
        cin>>l>>r;
        ans.push_back(num.search(l,r));
    }
    rep(i,0,q){
        cout<<ans[i]<<endl;
    }
}