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 "bits/stdc++.h"

using namespace std;

typedef long long ll;
typedef pair<int,int> P;
const double EPS = 1e-12;
const int INF = numeric_limits<int>::max()/2;
const int MOD = 1e9+7;

// sieve of eratosthenes
// primes[i] != 0 if i is prime
vector<int> sieve_of_eratosthenes(int n) {
  vector<int> primes(n);
  for (int i = 2; i < n; ++i)
    primes[i] = i;
  for (int i = 2; i*i < n; ++i)
    if (primes[i])
      for (int j = i*i; j < n; j+=i)
        primes[j] = 0;
  return primes;
}

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);

    int q;cin>>q;
    vector<int> primes=sieve_of_eratosthenes(111111);
    vector<int> res(111111,0);
    for(int i=3;i<111111;i+=2){
        if(primes[i] && primes[(i+1)/2]){
            res[i]=1;
            //cout<<i<<endl;
        }
    }
    for(int i=3;i<111111;i++){
        res[i]+=res[i-1];
    }
    for(int i=0;i<q;i++){
        int l,r;cin>>l>>r;
        cout<<res[r]-res[l-1]<<endl;
    }
}