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

def is_prime(n):
    if n <= 1:
        return False
    if n == 2:
        return True
    if n % 2 == 0:
        return False
    for i in range(3, math.ceil(math.sqrt(n))+1, 2):
        if n % i == 0:
            return False
    return True


# 素数を表にする
primetable = [ 0 for i in range(3000) ]
for i in range(2, 3000):
    if is_prime(i):
        primetable[i] = 1
# 2017に似た数を表にする
like2017table = [ 0 for i in range(3000) ]
for i in range(2, 3000):
    if primetable[i] == 1 and \
        primetable[(i+1)//2] == 1:
        like2017table[i] = 1


n = int(input())
queries = []
for _ in range(n):
    queries.append(list(map(int, input().split())))

for query in queries:
    begin = query[0]
    end = query[1]
    ans = sum(like2017table[begin:end+1])
    print(ans)