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 (2.7.6) (judge verdict: Wrong Answer)

#!/usr/bin/python

import math
import sys

def is_prime(n):
    if n == 1:
        return False

    for i in xrange(2, int(math.sqrt(n)) + 1):
        if n % i == 0:
            return False
    return True

def main(argv):
    primes = []
    for i in xrange(1, 10000 + 1):
        primes.append(is_prime(i))

    results = [0]
    for i in xrange(1, 10000 + 1):
        if primes[i - 1] and primes[(i + 1) / 2 - 1]:
            results.append(1)
        else:
            results.append(0)

    line = sys.stdin.readline()
    while line:
        Q = int(line.rstrip("\n"))
        for i in xrange(Q):
            l, r = map(
              lambda i: int(i), sys.stdin.readline().rstrip("\n").split(" "))

            print sum(results[l:r+1])

        line = sys.stdin.readline()

if __name__ == "__main__":
    main(sys.argv)