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;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep2(i, s, n) for (int i = (s); i < (int)(n); i++)
typedef long long ll;

int main() {
    vector<int> prime;
    prime.push_back(2);
    bool flag;
    for (int i = 3; i <= 100000; i++) {
        flag = true;
        for (int j = 0; j < prime.size(); j++) {
            if (prime[j] * prime[j] > i) break;
            else if (i % prime[j] == 0) {
                flag = false;
                break;
            }
        }
        if (flag) prime.push_back(i);
    }

    vector<int> prime2;
    for (int i = 0; i < prime.size(); i++) {
        if (binary_search(prime.begin(), prime.end(), (prime[i]+1)/2)) prime2.push_back(prime[i]);
    }
    
    int Q; cin >> Q;
    int l, r;
    for (int i = 0; i < Q; i++) {
        cin >> l >> r;
        cout << upper_bound(prime2.begin(), prime2.end(), r) - lower_bound(prime2.begin(), prime2.end(), l) << endl;
    }

}