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)

numq = int(input())
lis = [1]*100001
lis[0] = 0
lis[1] = 0
i = 2
while(i < 318):
  if lis[i] == 1:
    k = 2
    while(i*k < 100001):
      lis[i*k] = 0
      k += 1
  i += 1
lis2 = [0]*100001

for i in range(1,100001):
  if i % 2 == 1 and lis[i] == lis[(i+1)//2] == 1:
    lis2[i] = lis2[i-1] + 1
  else:
    lis2[i] = lis2[i-1]

for _ in range(numq):
  a,b = map(int,input().split())
  print(lis2[b] - lis2[a-1])