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)

def net(end_num):
    if end_num < 2:
        return []
    primes = [2]
    nums = list(range(3, end_num, 2))
    while nums:
        primes.append(nums[0])
        nums = [n for n in nums if n % nums[0]]
    return primes

cumsum = []
sum_val = 0
primes = net(330)
for n in range(0, 100001):
    like_2017 = True
    for p in primes:
        if (n % p == 0) and (n > p):
            like_2017 = False
            break
        if (((n + 1) // 2) % p == 0) and (((n + 1) // 2) > p):
            like_2017 = False
            break
    sum_val += like_2017
    cumsum.append(sum_val)
    
for _ in range(int(input())):
    l, r = map(int, input().split())
    print(cumsum[r] - cumsum[l - 1])