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 <string.h>
#define M 100000

int main(){
	int Q,l,r,i,j,a=0;
	int nprime[M+1]={};
	int num[M+1]={};
	int ans[M+1]={};
	
	nprime[0]=1;
	nprime[1]=1;
	
	for(i=2;i<=M;i++){
		for(j=2;j*i<=M;j++){
			nprime[i*j]=1;
		}
	}
	
	for(i=2;i<=M;i++){
		if((i%2)&&(!nprime[i])&&(!nprime[(i+1)/2])) a++;
		num[i]=a;
	}
	
	scanf("%d",&Q);
	for(i=1;i<=Q;i++){
		scanf("%d %d",&l,&r);
		ans[i]=num[r]-num[l-1];
	}
	for(i=1;i<=Q;i++) printf("%d\n",ans[i]);
	return 0;
}