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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <iostream>
#include <string>
#include <algorithm>
#include <iterator>
#include <functional>
#include <vector>
#include <math.h>
using namespace std;

struct obj 
{
	int l;
	int r;
};


vector<bool> prime(100000, true);

void createPrime()
{	
	prime[0] = false;
	prime[1] = false;	

	double sqrtNum = sqrt(100000 * 1.0);
	for (int i = 2; i < sqrtNum; i++)
	{
		if (prime[i] == false)
		{
			continue;
		}

		for (int j = i * i; j < 100000; j+=i)
		{
			prime[j] = false;
		}
	}

}

int main(void) {
	
	int N;
	cin >> N;

	vector<obj> list(N);

	for (int i = 0; i < N; i++)
	{
		cin >> list[i].l >> list[i].r;
	}

	createPrime();

	for (int i = 0; i < N; i++)
	{
		int ans = 0;
		for (int j = list[i].l; j <= list[i].r; j+=2)
		{				
			if (prime[j] && prime[(j + 1) / 2])
			{
				ans++;
			}
		}
		cout << ans << endl;
	}

	return 0;
}