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 sys
read = sys.stdin.buffer.read
input = sys.stdin.readline
#input = sys.stdin.buffer.readline

#sys.setrecursionlimit(10**9)

def RD(): return sys.stdin.read()
def II(): return int(input())
def MI(): return map(int,input().split())
def MF(): return map(float,input().split())
def LI(): return list(map(int,input().split()))
def LF(): return list(map(float,input().split()))
def TI(): return tuple(map(int,input().split()))
# rstrip().decode('utf-8')

#2335

def main():
	n = 10**5+10
	primes = set(range(2, n+1))
	for i in range(2, int(n**0.5+1)):
		primes.difference_update(range(i*2, n+1, i))

	li=set()
	for i in primes:
		li.add(i)
		if i*2<n:
			li.add(i*2)
	li=list(li)
	li.sort()
	#print(li)

	li2=[0]*(n)
	for i in range(len(li)-1):
		if li[i]%2==1 and li[i+1]==li[i]+1:
			li2[li[i]]=1
	#print(li2)

	for i in range(n-1):
		li2[i+1]+=li2[i]
	#print(li2)

	q=II()
	for _ in range(q):
		l,r=MI()
		print(li2[r]-li2[l-1])





if __name__ == "__main__":
	main()