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.Arrays;
import java.util.Scanner;
import java.util.stream.IntStream;

/**
 * 解説どおりに作成したソースコード
 */
public class Main {

	/** 計算する最大値 */
	private static final int N = 100_000;

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			// Nまでの素数を計算する
			boolean[] isPrime = new boolean[N + 1];
			Arrays.fill(isPrime, true);
			isPrime[0] = isPrime[1] = false;
			IntStream.rangeClosed(2, N).forEach(i -> {
				if (isPrime[i]) {
					IntStream.rangeClosed(2, N / i).forEach(j -> isPrime[j * i] = false);
				}
			});
			// 最大値まで2017に似た数を計算する
			int[] count = new int[N];
			count[0] = count[1] = count[2] = 0;
			IntStream.range(3, N).forEach(i -> count[i] = count[i - 1] + (is2017LikeNumber(i, isPrime) ? 1 : 0));
			int q = scanner.nextInt();
			IntStream.range(0, q).map(i -> {
				int l = scanner.nextInt();
				int r = scanner.nextInt();
				return count[r] - count[l - 1];
			}).forEach(System.out::println);
		}
	}

	/**
	 * 入力数字が2017に似た数であるかどうかを計算
	 * 
	 * @param number  入力数字
	 * @param isPrime indexが素数かどうかの配列
	 * @return 入力数字が2017に似た数であるかどうか
	 */
	private static boolean is2017LikeNumber(int number, boolean[] isPrime) {
		return (1 == (number & 1)) && isPrime[number] && isPrime[(number + 1) / 2];
	}
}