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: Wrong Answer)

import math
from itertools import accumulate

def primes(n):
  prime = ([False]*2) + ([True]*(n-2))
  for i in range(2, int(math.sqrt(n))+1):
    if prime[i]:
      for j in range(i*2, int(math.sqrt(n))+1, i):
        prime[j] = False
  return prime

MAX = (10**5)+1
is_prime = primes(MAX)
q = int(input())
A = [1 if is_prime[i] and is_prime[(i + 1)//2] else 0 for i in range(MAX)]
S = [0] + list(accumulate(A))

Q = []
Q_append = Q.append
for _ in range(q):
    l, r = map(int, input().split())
    Q_append((l, r))

for qi in Q:
    print(S[qi[1]+1]-S[qi[0]])