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)

# 毎回やってもたかがしれてそう -> 間に合いませんでした
# 素直に累積和+包除原理を使う

arr = [0 for _ in range(10 ** 5 + 1)]


def isPrime(x):
    if x == 1:
        return False
    for i in range(2, int(x ** 0.5) + 1):
        if x % i == 0:
            return False
    return True


for i in range(3, 10**5+1):
    if isPrime(i) and isPrime(int((i + 1) / 2)):
        arr[i] = 1
    arr[i] += arr[i-1]

q = int(input())


for _ in range(q):
    l, r = map(int, input().split())
    print(arr[r] - arr[l-1])