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 Fortran (gfortran v4.8.4) (judge verdict: Time Limit Exceeded)

program D_solution

implicit none
integer :: Q,l(10**5),r(10**5)
integer :: i,j
integer :: is_prime(10**5),like_2017(50001)

read(*,*) Q
do i = 1, Q
  read(*,*) l(i),r(i)
enddo

is_prime(1) = 0

do i = 2, 10**5
  is_prime(i) = 1
  do j = 2, int((i)**0.5)
    if(mod(i,j) == 0) then
      is_prime(i) = 0
    endif
  enddo
enddo

like_2017 = 0

do i = 1, 10**5, 2
  like_2017((i+1)/2) = is_prime(i) * is_prime((i+1)/2)
enddo

do i=1,Q
    write(*,*) sum(like_2017((l(i)+1)/2:(r(i)+1)/2))
enddo
end program