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: Accepted)

import java.util.Scanner;

public class Main {

	static Scanner sc = new Scanner(System.in);

	public static void main(String[] args){

		solve_2020_0217_002();
	}



	public static void solve_2020_0217_002(){


		int max = 101010;

		//prime number
		boolean[] isPrime = new boolean[max];
		for(int i=2;i<max;i++) isPrime[i] = true;
		for(int i=2; i<max; i++){
			if(!isPrime[i]) continue;
			for(int j=2;j*i<max;j++){
				isPrime[j*i] = false;
			}
		}

		//2017-like number
		int[] isLikeNum = new int[max];
		for(int i=3; i<max; i=i+2){
			if(isPrime[i] && isPrime[(i+1)/2]){
				isLikeNum[i] = 1;
			}
		}

		//cumulative sum
		int[] cs = new int[max];
		for(int i=1;i<max;i++){
			cs[i] = cs[i-1] + isLikeNum[i];
		}

		int Q =sc.nextInt();
		int[] numLikeNumber = new int[Q];

		for(int i=0;i<Q;i++){

			int l = sc.nextInt();
			int r = sc.nextInt();
			numLikeNumber[i] = cs[r]-cs[l-1];
		}

		for(int nLN: numLikeNumber) System.out.println(nLN);
	}
}