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: Accepted)

import itertools
q = int(input())
left = []
right = []
for _ in range(q):
    l, r = map(int, input().split())
    left.append(l)
    right.append(r)

def check(n):
    root = int(n ** 0.5)
    if n == 1:
        return False
    elif n == 2:
        return True
    for i in range(2, root + 2):
        if n % i == 0:
            return False
    return True

upper = max(right)
f = [0, 0]
for i in range(3, upper + 1):
    if i % 2 == 0:
        f.append(0)
    elif check(i) and check((i + 1) // 2):
        f.append(1)
    else:
        f.append(0)
cumsum = list(itertools.accumulate(f))
for l, r in zip(left, right):
    if l == 1:
        print(cumsum[r - 1])
    else:
        print(cumsum[r - 1] - cumsum[l - 2])