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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;


public class Main {
    static void count2017ish(int l, int r){
        int count = 0;
        for(int i = l; i <= r; i+=2){
            if(i == 1){
                continue;
            }

            int ip = (i+1)/2;
            boolean ipIsPrime = true;
            int p = 2;
            while(Math.pow(p, 2) <= ip){
                if(ip % p == 0){
                    ipIsPrime = false;
                    break;
                }
                p++;
            }
            if(ipIsPrime){
                p = 2;
                boolean iIsPrime = true;
                while(Math.pow(p, 2) <= i){
                    if(i % p == 0){
                        iIsPrime = false;
                        break;
                    }
                    p++;
                }
                if(iIsPrime){
                    count++;
                }
            }
        }
        System.out.println(count);
    }

    static void solve(){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();

        for(int i = 0; i < n; i++){
            int l = sc.nextInt();
            int r = sc.nextInt();
            count2017ish(l, r);
        }

    }

    public static void main(String[] args){
        solve();
    }
}