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 PyPy3 (7.3.0) (judge verdict: Accepted)

Q=  int(input())
dp = [False]*(100001)
for i in range(2,100001):
    if not dp[i]:
        for j in range(2*i,100001,i):
            dp[j] = True
A = []
for i in range(3,100001):
    if not dp[i] and not dp[(i+1)//2]:
        A.append(i)
from bisect import bisect_left, bisect_right
queries = []
for _ in range(Q):
    l,r = map(int,input().split())
    queries.append([l,r])
for l,r in queries:
    idl = bisect_left(A,l)
    idr = bisect_right(A,r)
    print(idr-idl)