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)

Q = int(input())
l = []
r = []

for i in range(Q):
    L, R = map(int, input().split(" "))
    l.append(L)
    r.append(R)

for i in range(Q):
    a = [x for x in range(l[i], r[i]+1) if x%2 == 1 and x >= 3]
    counter = 0
    for j in a:
        for k in range(3, j+1, 2):
            if j%k == 0 and j//k != 1:
                break
            if ((j+1)/2)%2 == 0 and ((j+1)/2) != 2:
                break
            if ((j+1)/2)%k == 0 and ((j+1)/2)//k != 1:
                break
            if k+2 > j+1:
                counter += 1
                break
    print(counter)