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++ (GCC 9.2.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;


int main(){
  int MAX = 101010;
  vector<int> is_prime(MAX, 1);
  is_prime[0] = 0; is_prime[1] = 0;
  
  for(int i=2; i<MAX; ++i){
    if(!is_prime[i]) continue;
    for(int j=i*2; j<MAX; j+=i) is_prime[j]=0;
  }
  
  vector<int> a(MAX, 0);
  
  for(int i=0; i<MAX; ++i){
    if(i%2==0) continue;
    if(is_prime[i] && is_prime[(i+1)/2]) a[i] = 1;
  }
  
  vector<int> s(MAX+1, 0);
  for(int i=0; i<MAX; ++i) s[i+1] =s[i] + a[i];
  
  int Q; cin >> Q;
  
  for(int i=0; i<Q; i++){
    int l, r;
    cin >> l >> r;
    ++r;
    cout << s[r] - s[l] << endl;
  }
  
  return 0;
}