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;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			int q = int.Parse(Console.ReadLine());

			int max = 100001;
			var primes = new bool[max];
			for (int i = 2; i < max; i++) {
				primes[i] = true;
			}

			for (int i = 2; i < max; i++) {
				if (primes[i] == false) {
					continue;
				}

				int num = i * 2;
				while (num < max) {
					primes[num] = false;
					num += i;
				}
			}

			int[] ok = new int[max];
			for (int i = 3; i < max; i++) {
				if (primes[i] && primes[(i + 1) / 2]) {
					ok[i] = 1;
				}
			}

			var ruis = new int[max + 1];
			for (int i = 0; i < max; i++) {
				ruis[i + 1] = ruis[i] + ok[i];
			}

			var sb = new StringBuilder();
			for (int i = 0; i < q; i++) {
				var lr = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
				int val = ruis[lr[1] + 1] - ruis[lr[0]];
				sb.AppendLine(val.ToString());
			}

			Console.Write(sb.ToString());
		}
	}
}