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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>


#define dhai_machli ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define endl "\n"
#define ll long long
#define pii pair<int,int>
#define all(x) begin(x), end(x)
#define loop(i,n) for(int i=0; i<n; i++)
#define rep(i,a,b,c) for(int i=a; i<b; i+=c)
#define brep(i,a,b,c) for(int i=a; i>b; i-=c)
#define tc(t) int t; cin>>t; while(t--)
#define sz(v) int((v).size())
#define pb push_back

const int N = 2e5 + 10;


bool f[100001];
int c[100002];

int n, l, r;

using namespace std;

int main()
{



   dhai_machli;



   for ( int i = 2; i * i <= 100000; i ++) if (! f [ i ]) 
      for ( int j = i * i ; j <= 100000; j += i )
            f[ j ] = true ;
   for ( int i = 3; i <= 100000; i += 2) 

      if (! f [ i ] && ! f [( i + 1) / 2]) c [ i ]++;

   for ( int i = 3; i <= 100000; i ++) c [ i ] += c [i - 1];

      
   cin >> n;
   while (n--)
   {
      cin >> l >> r;

      cout << c[r] - c[l - 1] << endl;
   }


   return 0;
}