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)

#!/usr/bin python3
# -*- coding: utf-8 -*-
import sys
input=sys.stdin.readline
n = 10**5
#primes = set(range(3, n+1, 2))|set([2])
primes = set(range(3, n+1, 2)) #偶数は除く
for i in range(3, int(n**0.5+1)):
    primes.difference_update(range(i*3, n+1, i*2))
primes.add(2)

Likes = [0] * (n+1)
cnt = 0
for i in range(1,n+1,2):
    Likes[i-1]=Likes[i-2]
    x = (i+1)//2
    if i in primes and (x in primes or x==2):
        Likes[i]=Likes[i-1] + 1
    else:
        Likes[i]=Likes[i-1]

def main():
    Q = int(input())
    for q in range(Q):
        l,r = map(int,input().split())
        print(Likes[r]-Likes[l-1])

if __name__ == '__main__':
    main()