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<(n);i++)
#define rep1(i,n) for(ll i=1;i<=(n);i++)
#define all(x) (x).begin(),(x).end()
#define V vector
typedef V<int> vi;
typedef V<vi> vvi;
typedef long long ll;
typedef pair<int, int> P;
typedef tuple<int, int, int> T;
constexpr auto INF = INT_MAX >> 1;
constexpr auto LINF = 5000000000000000;
constexpr auto MOD = 1000000007;

vi prime, mnpf;
void preprime(int n) {

	prime.resize(0);
	mnpf.assign(n + 1, 1);
	rep1(i, n) {
		if (i < 2)continue;
		if (mnpf[i] != 1)continue;

		prime.push_back(i);
		mnpf[i] = i;
		int ii = i;
		while (ii <= n) {
			if (mnpf[ii] == 1)mnpf[ii] = i;
			ii += i;
		}
	}
}

int main() {
	
	preprime(102000);
	int q;
	cin >> q;

	vi like(0);
	for(auto x:prime) {
		if (x == 2)continue;
		if (binary_search(all(prime),(x+1)/2))like.push_back(x);
	}

	rep(i, q) {
		int l, r;
		cin >> l >> r;
		cout << upper_bound(all(like), r) - lower_bound(all(like), l) << endl;
	}

}