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: Wrong Answer)

from itertools import accumulate
V = [1]*(10**5+1)
P = [0]*(10**5+1)
V[0] = 0
V[1] = 0
for i in range(10**5+1):
    if V[i] == 0:
        continue
    P[i] = 1
    for j in range(2,(10**5+1)//i, i):
        V[i*j] = 0
W = [0]*(10**5+1)
for i in range(10**5+1):
    if not V[i]:
        continue
    if V[(i+1)//2] == 1:
        W[i] = 1
accW = list( accumulate(W))
Q = int( input())
for i in range(Q):
    l, r = map( int, input().split())
    print(accW[r] - accW[l-1])