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 <stdio.h>
#include <math.h>
#define MAX 1000000

void sieve();
char arr[MAX];

int main(){
    sieve();
    int n,i,l,j,count;
    scanf("%d",&n);
    while(n--){
        count=0;
        scanf("%d %d",&i,&l);
        for(j=i;j<=l;j+=2){
            if(arr[j]=='1' && arr[(j+1)/2]=='1') count++;
        }
        printf("%d\n",count);
    }
    return 0;

}

void sieve(){
    int i,j,k;
    arr[0]='0';
    arr[1]='0';
    for(i=2;i<=MAX;i++) arr[i]='1';
    k=sqrt(MAX);
    for(i=2;i<=k;i++){
        if(arr[i]=='1'){
            for(j=i;i*j<=MAX;j++){
                arr[i*j]='0';
            }
        }
    }
}