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: Accepted)

#include<stdio.h>
#include<stdlib.h>
 
int main(){
  int Q, l[100000], r[100000], i, j, P[100001], R[100001], S[100001];
  scanf("%d", &Q);

  for(i=0; i<Q; i++){
    scanf(" %d%d", &l[i], &r[i]);
  }

  P[0]=0; P[1]=0;
  for(i=2; i<=100000; i++)P[i]=1;

  for(i=2; i<=100000; i++){
    if(P[i]==1){
      for(j=2*i;j<=100000;j+=i)P[j]=0;
    }    
  }

  R[0]=0; R[1]=0;
  for(i=2; i<=100000; i++){
    if(P[i] & P[(i+1)/2])
      R[i]=1;
    else
      R[i]=0;
  }

  S[0]=0; S[1]=0;
  for(i=2; i<=100000; i++){
    S[i]=S[i-1]+R[i];
  }
  
  for(i=0; i<Q; i++){
    printf("%d\n",S[r[i]]-S[l[i]-1]);
  }

}