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: Wrong Answer)

import java.util.*;

class Main
{
    public static int[] prime = new int[10000];
    public static int[] like = new int[10000];
    public static int index1 = 0;
    public static int index2 = 0;

    public static 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();
        }

        Prime();
        LikeMake();

        for(int i = 0; i < Q; i++){
            int L_index = Arrays.binarySearch(like, L[i]);

            if(L_index < 0){
                L_index = (-1) * L_index - 1; 
            }

            int R_index = Arrays.binarySearch(like, R[i]);

            if(R_index < 0){
                R_index = (-1) * R_index  - 2;
            }
            System.out.println(L_index + " " + R_index);
            System.out.println( R_index - L_index + 1);
        }
    }
    static void Prime() // 素数生成
    {
        boolean bl = true;
    
        prime[0] = 2;

        for(int i = 1; i < 10000; i++){
            prime[i] = 1000007;
        }

        for(int num = 3; num < prime.length; num += 2){
            bl = true;;
            for(int j = 0; Math.pow(prime[j], 2) <= num; j++){
                if( num % prime[j] == 0){
                    bl = false;
                    break;
                }
            }
            if(bl == true){
                prime[++index1] = num;
            }
        }
    }
    static boolean LikeJudge(int p)
    {
        boolean ans = false;            
        if( Arrays.binarySearch(prime, (p + 1) / 2) >= 0){
            ans = true;
        }
        return ans;
    }
    
    static void LikeMake()
    {
        for(int i = 0; i < like.length; i++){
            like[i] = 10000;
        }
        for(int i = 1; i < prime.length; i++){
            if(LikeJudge(prime[i]) == true){
                like[index2] = prime[i];
                index2++;
            }
        }
    }
}