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 <bits/stdc++.h>
using namespace std;
struct queries{
	int l,r;
};
int main()
{
	int q;
	cin>>q;
	queries a[q+1];
	
	int maxv=1e-6,i,j,k;
	
	for(i=1;i<=q;i++)
	{
		cin>>a[i].l>>a[i].r;
		if(a[i].r>maxv)
		maxv=a[i].r;
	}
	
	bool is_prime[maxv+1];
	
	for(i=1;i<=maxv;i++)
	is_prime[i]=true;
	
	is_prime[0]=false;
	is_prime[1]=false;
	
	for(i=3;i<=maxv;i+=2)
	{
		if(is_prime[i])
		{
			for(j=3*i;j<=maxv;j+=2*i)
			is_prime[j]=false;
		}
	} 
	for(j=2;j<=maxv/2;j++)
	{
		is_prime[2*j]=false;
	}
	int sum=0;
	for(i=1;i<=q;i++)
	{
		sum=0;
		for(j=a[i].l;j<=a[i].r;j+=2)
		{
			if(is_prime[j]&&is_prime[(j+1)/2])
				sum++;
		}
		cout<<sum<<endl;
	}
	return 0;
}