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>
#include<math.h>
#include<string.h>
int p[111111]={};
void Furui(){
  for(int i=2;i<334;i++){
    if(p[i]==1){
      for(int j=i*2;j<111111;j+=i)p[j]=0;
    }
  }
}
int main(){
  for(int i=2;i<111111;i++)p[i]=1;
  Furui();
  int q;
  scanf("%d",&q);
  int x[111111]={};
  for(int i=2;i<55555;i++){
    if(p[i]==1){
      if(p[2*i-1]==1){
        x[2*i-1]=1;
      }
    }
  }
  for(int i=1;i<111111;i++)x[i]+=x[i-1];
  for(int i=0;i<q;i++){
    int l,r;
    scanf("%d%d",&l,&r);
    printf("%d\n",x[r]-x[l-1]);
  }
  return 0;
}