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)


Q = int(input())
N = 10**5 + 1000

def getPrimes():
    isPrime = [True] * N
    isPrime[1] = False
    for i in range(2, N):
        if not isPrime[i]:
            continue
        for p in range(i + i, N, i):
            isPrime[p] = False
    return isPrime

isPrime = getPrimes()

A = [0] * (N)
for i in range(2, N):
    if i % 2 == 1 and isPrime[i] and isPrime[(i + 1) // 2]:
        A[i] = 1
accA = [0] * (N + 1)
for i, a in enumerate(A, start=0):
    accA[i] += accA[i - 1] + a

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