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: Runtime Error)

maxnum = 10001

# エラトステネスのふるい
is_prime = [x for x in range(maxnum)]
for prime in is_prime:
    if prime == 0 or prime == 1:
        is_prime[prime] = 0
        continue
    for non_prime in range(prime * 2, maxnum, prime):
        is_prime[non_prime] = 0

is_like = [False] * maxnum
for i in range(maxnum):
    if (is_prime[i] and is_prime[(i + 1) // 2]):
        is_like[i] =  True

like_sum = [0] * maxnum
for i in range(1, maxnum):
    like_sum[i] = like_sum[i - 1]
    if (is_like[i]):
        like_sum[i] += 1

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