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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

vector<ll> primes(100020), w(100020);
vector<ll> v;

int main() {
  
  ll count = 0;
  ll j;
  
  for ( ll i = 2; i < 100020; i++ ){
    
    bool ok = true;
    for ( j = 0; primes[j] * primes[j] <= i && j < count; j++) {
      if ( i % primes[j] == 0 ){
        ok = false;
        break;
      }
    }
    
    if ( !ok ) continue;
    primes[count++] = i;
  }
  
  for ( ll i = 1; i < count; i++ ){
    if ( find(primes.begin(), primes.end(), (primes[i] + 1) / 2) != primes.end() )
      v.push_back(primes[i]);
  }
  
  ll pos = 0;
  for ( ll i = 1; i < count; i++ ){
    w[i] = w[i-1];
    if ( i == v[pos] ) {
      pos++;
      w[i]++;
    }
  }
  
  ll q;
  cin >> q;
  ll l, r;
  for ( ll i = 0; i < q; i++ ){
    cin >> l >> r;
    cout << w[r] - w[l-1] << endl;
  }
  
}