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)

f=[True]*(10**5+1)
like=[False]*(10**5+1)
f[0]=False
f[1]=False
import math
for i in range(2,len(f)):
  fact=True
  for j in range(2,int(math.sqrt(i))+1):
    if i%j==0:
      fact=False
      break
  
  if fact:
    f[i]=True
    if i*2-1<len(like):
      like[i*2-1]=True
    for p in range(i*2,len(f),i):
      f[p]=False

sums=[0]*(10**5+1)
cur=0
for i in range(len(sums)):
  if f[i] and like[i]:
    sums[i]=cur+1
    cur+=1
  else:
    sums[i]=cur

Q=int(input())
for i in range(Q):
  l,r=map(int,input().split())
  if l>0:
    print(sums[r]-sums[l-1])
  else:
    print(sums[r])