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: Memory Limit Exceeded)


import java.util.*;

public class Main{

    BitSet primes;
    private void primesOfEratosthenes(int n){
        int rn = (int)Math.sqrt(n);

        primes = new BitSet(n+1);
        primes.flip(0,n+1);

        primes.set(0,false);
        primes.set(1,false);
        for(int i=4;i<primes.size();i+=2){
            primes.set(i,false);
        }

        int i=3;
        while(true){
            for(int j=i;i*j<primes.size();j+=2){
                primes.set(i*j,false);
            }

            i = primes.nextSetBit(i+1);
            if(i>rn){
                break;
            }
        }
    }

    BitSet like2017s;
    private void precalc(){
        like2017s = (BitSet)primes.clone();

        for(int i=like2017s.nextSetBit(2); i!=-1 ; i=like2017s.nextSetBit(i+1)){
            int n = (int)((i+1)/2);
            like2017s.set(i,primes.get(n));
        }
    }

    private int solve(int l, int r){
        return like2017s.get(l,r+1).cardinality();
    }

    private void _main(String[] args){
        Scanner sc = new Scanner(System.in);
        int q = sc.nextInt();
        int[] l = new int[q];
        int[] r = new int[q];

        for(int i=0;i<q;i++){
            l[i] = sc.nextInt();
            r[i] = sc.nextInt();
        }

        int max=0;
        for(int i=0;i<q;i++){
            max = Math.max(r[i], max);
        }
        primesOfEratosthenes(max);
        precalc();

        for(int i=0;i<q;i++){
            System.out.println(solve(l[i], r[i]));
        }

        sc.close();
    }

    public static void main(String[] args){
            (new Main())._main(args);
    }
}