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)

MAX_PRIME = 10**5
is_prime = [1] * MAX_PRIME
primes = set()
is_prime[0] = 0
is_prime[1] = 0
for i in range(MAX_PRIME):
    if is_prime[i]:
        primes.add(i)
        for j in range(2, ((MAX_PRIME-1)//i) + 1):
            is_prime[i*j] = 0
yearlike = set()
for i in range(1,10**5):
    if i in primes and (i+1)//2 in primes:
        yearlike.add(i)
cum = [0] * 2*10**5
for i in range(10**5+5):
    cum[i+1] = cum[i] + int(i in yearlike)
q = int(input())
query = [tuple(map(int, input().split())) for _ in range(q)]
for l, r in query:
    print(cum[r+1] - cum[l])