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: Time Limit Exceeded)

# -*- coding: utf-8 -*-
q = int(input())
ql = []
R = 0
for _ in range(q):
    l,r = map(int, input().split())
    ql.append((l,r))
    R = max(R,r)
R += 1

is_prime = [True]*(R+1)
is_prime[0] = False
is_prime[1] = False
for n in range(2,R+1):
    if is_prime[n]:
        x = 2
        while n*x<R+1:
            is_prime[n*x] = False
            x += 1
primes = []
for i in range(len(is_prime)):
    if is_prime[i]:
        primes.append(i)

like2017 = [0]*(R+1)
for i in range(R):
    if i%2==1 and (i in primes) and ((i+1)//2 in primes):
        like2017[i+1] = like2017[i] + 1
    else:
        like2017[i+1] = like2017[i]

for (l,r) in ql:
    print(like2017[r+1] - like2017[l])