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)

import sys
from collections import deque
from bisect import bisect_left
input = sys.stdin.readline
Q = int(input())
P = 10 ** 5
c1 = [(i+1) % 2 == 1 for i in range(P)]
c2 = [False for i in range(P)]
c2[2] = True
L = deque([])
for i in range(2, P):
    if c1[i]:
        ind = (i+1)*2-2
        if ind < P:
            c2[ind] = True
    if c1[i] and c2[i]:
        L.append(i+1)
        ind = (i+1) * 2 - 1
        while ind < P:
            c1[ind] = False
            ind += (i+1)

for q in range(Q):
    l, r = [int(x) for x in input().strip().split()]
    print(bisect_left(L, r+1) - bisect_left(L, l))