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: Accepted)

def eratosthenes(n):
 is_p=[1]*n
# p_list=[]

 is_p[0]=0
 is_p[1]=0

 for i in range(2,n):
  if is_p[i]:
#   p_list.append(i)
   for j in range(i*i,n,i):
    is_p[j] = 0

 return is_p#, p_list

lim=10**5+1
#is_p, p_list=eratosthenes(lim)
is_p=eratosthenes(lim)

q=int(input())

'''
b=[0]
for i in range(1,lim+1):
 if is_p[i-1] and is_p[i//2]:
  b.append(b[i-1]+1)
 else:
  b.append(b[i-1])
'''
a = [0] * (10**5+2)
for i in range(3, 10**5+1, 2):
    if is_p[i] and is_p[(i+1)//2]:
        a[i] = 1
for i in range(1, 10**5+1):
    a[i+1] += a[i]

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