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>
#define rep(i, n) for (int i=0; i<(n); i++)
#define ll long long
using namespace std;

const int MAX_N=100000;

bool is_prime[MAX_N+1];
bool is_2017[MAX_N+1];
int P[MAX_N+1];

void sieve() {
  for (int i=0; i<=MAX_N; i++) is_prime[i]=true;
  is_prime[0]=is_prime[1]=false;
  for (int i=2; i<=MAX_N; i++) {
    if (is_prime[i]) {
      for (int j=2*i; j<=MAX_N; j+=i) is_prime[j]=false;
    }
  }
}

void ok2017() {
  for (int i=0; i<=MAX_N; i++) is_2017[i]=false;
  for (int i=2; i<=MAX_N; i++) {
    int j=(i+1)/2;
    if (is_prime[i]&&is_prime[j]) is_2017[i]=true;
  }
}

int main() {
  int Q; cin>>Q;
  sieve();
  ok2017();
  rep(i, MAX_N+1) {
    if (is_2017[i]) P[i]++;
  }
  rep(i, MAX_N) P[i+1]+=P[i];

  vector<int> res;
  rep(query, Q) {
    int l,r; cin>>l>>r;
    int tmp=P[r]-P[l-1];
    res.push_back(tmp);
  }
  rep(i, Q) cout<<res[i]<<endl;
}