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 {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        boolean isPrime[] = new boolean[100001];
        for (int i = 0; i <= 100000; i++) {
            isPrime[i] = true;
        }
        isPrime[0] = false;
        isPrime[1] = false;
        for (long i = 2; i <= 100000; i++) {
            for (long j = i * 2; j <= 100000; j += i) {
                isPrime[(int) j] = false;
            }
        }

        boolean isLike2017[] = new boolean[100001];
        for (int i = 0; i <= 100000; i++) {
            isLike2017[i] = isPrime[i] && isPrime[(i + 1) / 2];
        }
        int sum[] = new int[100002];
        sum[0] = 0;
        for (int i = 0; i <= 100000; i++) {
            sum[i + 1] = sum[i];
            if (isLike2017[i]) {
                sum[i + 1]++;
            }
        }
        int n = in.nextInt();
        for (int i = 0; i < n; i++) {
            int l = in.nextInt();
            int r = in.nextInt();
            System.out.println(sum[r + 1] - sum[l]);
        }
    }
}