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: Time Limit Exceeded)

Q = int(input())

data = []
max_number = 0
for i in range(Q):
	x = input().split()
	data.append([int(x[0]),int(x[1])])
	if max_number<data[i][1]:
		max_number = data[i][1]


prime_arr = [2]

for i in range(3,max_number+100,2):
	c = 0
	for j in prime_arr:
		if j>i**0.5:
			break
		elif i%j==0:
			c = 1
	if c==0:
		prime_arr.append(i)

def judge(a):
	return ((a in prime_arr)) and (((a+1)/2 in prime_arr))

def sumz(a,b):
	x = 0
	y = 0
	for n in range(len(prime_arr)):
		if prime_arr[n]<a:
			x = n
		if prime_arr[n]>b:
			y = n
			break
	#print(x+1,y-1)
	#print(prime_arr[x+1],prime_arr[y-1])
	return sum(judge_arr[x+1:y])

judge_arr = [0]*len(prime_arr)
for n in range(len(prime_arr)):
	if prime_arr[n] in prime_arr and (prime_arr[n]+1)/2 in prime_arr:
		judge_arr[n] = 1


for x in range(Q):
	print(sumz(data[x][0],data[x][1]+1))