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.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner in = new Scanner(System.in);

        Set<Integer> P = makePrimes(100000);
        int[] S = new int[100001];
        int c = 0;
        for (int n = 1; n < 100001; n++) {
            if (P.contains(n) && P.contains((n + 1) / 2)) {
                c++;
            }
            S[n] = c;
        }

        int Q = in.nextInt();
        for (int q = 0; q < Q; q++) {
            int L = in.nextInt();
            int R = in.nextInt();
            System.out.println(S[R] - S[L - 1]);
        }
    }

    static HashSet<Integer> makePrimes(int n) {
        HashSet<Integer> P = new HashSet<>();
        boolean[] F = new boolean[n + 1];
        Arrays.fill(F, true);
        for (int i = 2; i < n + 1; i++) {
            if (!F[i]) {
                continue;
            }

            P.add(i);
            for (int j = i; j < n + 1; j += i) {
                F[j] = false;
            }
        }

        return P;
    }
}