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 Python (3.4.3) (judge verdict: Accepted)

import math
import sys
def sieve(n):
    if n < 2:
        is_prime = [False for _ in range(n+1)]
        return is_prime
 
    is_prime = [True for _ in range(n+1)]
    is_prime[0] = False
    is_prime[1] = False
 
    for i in range(2, int(n**0.5)+1):
        if is_prime[i]:
            for j in range(i*2, n+1, i):
                is_prime[j] = False
 
    return is_prime

def main():
	N=10**5
	prime=sieve(N)
	a=[0 for i in range(N+1)]
	for i in range(3,N+1):
		if prime[i] and prime[(i+1)//2]: a[i]=a[i-1]+1
		else: a[i]=a[i-1]

	Q=int(input())
	for i in range(Q):
		l,r=map(int,input().split())
		print(a[r]-a[l-1])


if __name__ == '__main__':
    main()