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;
using static System.Console;
using static System.Math;

namespace AtCodeeeer
{
    class AtCOOOOOOOOOOOder
    {
        //いつもの
        readonly static long mod = 1000000000 + 7;
        static void Main(string[] args)
        {
            int n = int.Parse(ReadLine());

            int[] CumulativeSums = Enumerable.Repeat(0, (int)Math.Pow(10, 5) + 1).ToArray();
            int[] CumulativeSums2 = Enumerable.Repeat(0, (int)Math.Pow(10, 5) + 1).ToArray();
            int hoge = 0;int tmp = 0;
            for (int i = 0; i <= (int)Math.Pow(10, 5); i++)
            {
                if (Is_Prime(i))
                {
                    if (Is_Prime( (i+1)/2 ))
                    {
                        hoge++;
                    }
                }
                CumulativeSums[i] = hoge;
            }

            for (int i = 0; i < n; i++)
            {
                int[] s = ReadLine().Split(' ').Select(int.Parse).ToArray();
                int l = s[0];
                int r = s[1];
                WriteLine(
                    (CumulativeSums[r] - CumulativeSums[l-1])
                    );

            }
        }

        /// <summary>
        /// 素数判定を行う関数
        /// 計算量はO(n)
        /// </summary>
        /// <param name="n">対象変数</param>
        /// <returns></returns>
        static bool Is_Prime(long n)
        {
            if (n == 2)
            {
                return true;
            }
            if (n < 2 || n % 2 == 0)
            {
                return false;
            }
            int i = 3;
            while (i <= Math.Sqrt(n))
            {
                if (n % i == 0)
                {
                    return false;
                }
                i += 2;
            }
            return true;
        }
    }
}