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 5.4.1) (judge verdict: Time Limit Exceeded)

#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstring>
using namespace std;
const int N=pow(10,5);

bool is_Prime(int x) {
  if (x==1) {
    return false;
  }
  if (x!=2 && x%2==0) {
    return false;
  }
  for (int i=3; i<=sqrt(x); i+=2) {
    if (x%i==0) {
      return false;
    }
  }
  return true;
}
int main() {
  bool lr_prime[N+1];
  memset(lr_prime,false,sizeof(lr_prime));
  for (int i=1; i<N+1; i++) {
    lr_prime[i]=is_Prime(i);
  }
  int Q;
  scanf("%d",&Q);
  int l, r;
  while (Q--) {
    int x=0;
    scanf("%d %d",&l,&r);
    for (int i=l; i<=r; i++) {
      if (lr_prime[i] && lr_prime[(i+1)/2]) {
        x++;
      }
    }
    printf("%d\n",x);
  }
  return 0;
}