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) {
    Scanner sc = new Scanner(System.in);
    int q = sc.nextInt();
    // 素数かどうかを表す
    int[] prime = new int[100001];
    for(int i = 2; i < 100001; i++) {
      int f = 1;
      for(int j = 2; j * j <= i; j++) {
        if((i % j) == 0) {
          f = 0;
          break;
        }
      }
      prime[i] = f;
    }
    // i以下の似た数の個数を表す
    int[] like = new int[100001];
    for(int i = 2; i < 100001; i++) {
      like[i] = like[i - 1];
      if(((i % 2) == 1) && (prime[i] == 1) && (prime[(i + 1) / 2] == 1)) like[i]++;
    }
    for(int i = 0; i < q; i++) {
      int l = sc.nextInt();
      int r = sc.nextInt();
      System.out.println(like[r] - like[l - 1]);
    }
  }
}