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 (3.8.2) (judge verdict: Accepted)

q = int(input())

n = 10**6
is_prime = [True]*(n+1)
is_prime[0] = False
is_prime[1] = False
for i in range(2, int(n**0.5) + 1):
	if not is_prime[i]:
		continue
	for j in range(i * 2, n + 1, i):
		is_prime[j] = False

P = [0]*(10**6)

for i in range(1,10**6 - 1):
	if is_prime[i+1] == True and is_prime[(i+2)//2] == True:
		P[i+1] = P[i] + 1
	else:
		P[i+1] = P[i]

for i in range(1,q+1):
	l,r = map(int,input().split())
	print(P[r] - P[l-1])