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)

def sieve(N):#エラトステネスの篩
    prime = [0]*(N+1)
    isprime = [True]*(N+1)
    isprime[0]=isprime[1] = False
    num = 0
    for p in range(2,N+1):
        if isprime[p]:
            prime[num] = p
            num += 1
            for j in range(2*p,N+1,p):
                isprime[j] = False
    return prime
from bisect import bisect_left as bl
from bisect import bisect_right as br
lis = sieve(10**5)
prime = set(lis)-{0}
for i in range(len(lis)):
    if lis[i] != 0:
        if (lis[i]+1)//2 in prime:continue
        else:lis[i] = 0
    else:continue
Q = int(input())
lis = set(lis)-{0}
lis = sorted(tuple(lis))
for _ in range(Q):
    l,r = map(int,input().split())
    t = bl(lis,l)
    s = br(lis,r)
    tmp = s-t
    print(tmp)