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: Accepted)

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <cmath>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <iomanip>
using namespace std;
typedef long long ll;
typedef vector<int> VI;
typedef vector<ll> VL;
typedef vector<string> VS;
typedef vector< vector<int> > VVI;
typedef vector< vector<ll> > VVL;
typedef pair<int,int> PII;
#define rep(i,n) for(int i=0;i<(n);i++)
#define all(a) (a).begin(),(a).end()
#define pb push_back
#define mp make_pair
#define ub upper_bound
#define lb lower_bound
 
int main(){
  int Q;
  cin>>Q;
  VI L(Q),R(Q);
  rep(i,Q) cin>>L[i]>>R[i];
  VI X(100100);
  rep(i,100100) if(i>1) X[i]=1;
  rep(i,100100){
    if(X[i]==1) rep(j,100100/i){
      if(i*(j+2)<100100) X[i*(j+2)]=0;
    }
  }
  VI B(100100);
  rep(i,100100) if(X[i] and X[(i+1)/2]) B[i]++;
  VI C(100100);
  rep(i,100100) if(i) C[i]=C[i-1]+B[i];
  rep(i,Q) cout<<C[R[i]]-C[L[i]-1]<<endl;
}