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<iostream>
#include<string>
#include<algorithm>
#include<cmath>
#include<vector>
#include<queue>
#include<set>
#include<map>

#define INF 1000000007
#define LINF 1000000000000000007

using namespace std;

typedef long long Int;
typedef pair<Int, Int> P;

Int gcd(Int x, Int y){
	if(y == 0)
		return x;
	return gcd(y, x % y);
}

Int lcm(Int x, Int y){
	return x * y / gcd(x, y);
}

bool sosuu(int x){
	bool b = 1;
	if(x == 1) b = 0;
	for(int i = 2; i * i <= x; i++){
		if(x % i == 0) {
			b = 0;
			break;
		}
	}
	return b;
}

Int n, l[100001], r[100001], cnt[100001] = {0}, d[100003] = {0};
bool b[100001] = {0};

int main(){
	for(int i = 1; i < 100001; i+=2){
		if(sosuu(i) && sosuu((i+1)/2)) b[i] = 1;
		d[i+2] = d[i] + b[i];
	}
	cin >> n;
	for(int i = 0; i < n; i++){
		cin >> l[i] >> r[i];
		cnt[i] = d[r[i]+2] - d[l[i]];
	}
	
	for(int i = 0; i < n; i++){
		cout << cnt[i] << endl;
	}
	
	return 0;
}