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: Accepted)

#include<bits/stdc++.h>
using namespace std;
int p[100009];
int f[100009];
main()
{
    p[1]=1;
 
    for (int i=2; i<=100000; i++)
    {
        for (int j=2*i; j<=100000; j+=i)
            p[j]=1;
    }
    p[2]=0;
    for (int i=1; i<=100000; i++)
    {
        if(p[i]==0 && p[(i+1)/2]==0 && i!=2)
            {
                f[i]=f[i-1]+1;
            }
        else f[i]=f[i-1];
    }
    int q;
    cin>>q;
    while(q--)
    {
        int l,r;
        cin>>l>>r;
        cout<<f[r]-f[l-1]<<endl;
    }
}