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.Scanner;
 
public class Main{
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int Q=sc.nextInt();
		int[][] queri = new int[Q][2];
		int[] memo = new int[100001];
		for(int i=0;i<Q;i++) {
			queri[i][0]=sc.nextInt();
			queri[i][1]=sc.nextInt();
		}
		for(int i=0;i<Q;i++) {
			int n=queri[i][0];
			int m=queri[i][1];
			int ans=0;
			while(n<=m) {
				if(n%2==1) {
					if(memo[n]>0) {
						ans+=1;
					}
					else if(isPrime(n) && isPrime((n+1)/2)) {
						memo[n]=10;
						ans+=1;
					}
				}
				n+=1;
			}
			System.out.println(ans);
		}
 
		sc.close();
    }
	public static boolean isPrime(int num) {
	    if (num < 2) return false;
	    else if (num == 2) return true;
	    else if (num % 2 == 0) return false; // 偶数はあらかじめ除く
 
	    double sqrtNum = Math.sqrt(num);
	    for (int i = 3; i <= sqrtNum; i += 2)
	    {
	        if (num % i == 0)
	        {
	            // 素数ではない
	            return false;
	        }
	    }
 
	    // 素数である
	    return true;
	}
}