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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

namespace kozaiyApp
{
    public class LikeNumber
    {
        static void Main()
        {
            int Q = int.Parse(Console.ReadLine());
            int[] left = new int[Q];
            int[] right = new int[Q];
            for (int i = 0; i < Q; i++)
            {
                string[] input = Console.ReadLine().Split(' ');
                left[i] = int.Parse(input[0]);
                right[i] = int.Parse(input[1]);
            }

            // 素数リスト、2017に似た数リストを作成
            int MAX = 100001;
            bool[] isPrimeNumbers = sieve(MAX);
            int[] likeNumbers = Enumerable.Repeat<int>(0, MAX).ToArray(); // trueなら1
            for (int i = 1; i < MAX; i++)
            {
                if (isPrimeNumbers[i] && isPrimeNumbers[(i + 1) / 2])
                {
                    likeNumbers[i] = 1;
                }
            }

            // 累積和の配列を作成
            int[] count = Enumerable.Repeat<int>(0, MAX).ToArray();
            for (int i = 1; i < MAX; i++)
            {
                count[i] = count[i - 1] + likeNumbers[i - 1];
            }

            // 出力
            for (int i = 0; i < Q; i++)
            {
                int r = right[i];
                int l = left[i];
                Console.WriteLine(count[r + 1] - count[l]);
            }
        }

        // エラトステネスの篩
        static bool[] sieve(int n)
        {
            bool[] isPrime = Enumerable.Repeat<bool>(true, n + 1).ToArray(); // iが素数ならtrue

            isPrime[0] = isPrime[1] = false;

            for (int i = 2; i <= n; i++)
            {
                if (isPrime[i])
                {
                    for (int j = 2 * i; j <= n; j += i) // 素数iの倍数を取り除く
                    {
                        isPrime[j] = false;
                    }
                }
            }

            return isPrime;
        }
    }
}