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)

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

import random
import sys

def is_prime(n, k=50):
    assert n > 0
    if n == 2:
        return True
    elif n == 1 or n % 2 == 0:
        return False
    # n - 1を2 ^ s * dの形にする
    d = n - 1
    s = 0
    while d % 2 == 0:
        d //= 2
        s += 1
    for i in range(k):
        a = random.randint(1, n - 1)
        if pow(a, d, n) != 1:
            for r in range(0, s):
                if pow(a, d * 2 ** r, n) == n - 1:
                    break
            else:
                return False
    return True

Q = int(input())
childs = [list(map(int, input().split())) for _ in range(Q)]

for c in childs:
    count = 0
    for n in range(c[0], c[1]+1):
        if is_prime(n) and is_prime((n+1)//2):
            count += 1
    print(count)