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 (GNU Fortran 9.2.1) (judge verdict: Accepted)

program prob4
    implicit none
    integer::p(100005), a(100005)
    integer::i, j, Q, l, r

    p = 0
    do i = 2, 100000
        if(p(i) == 0) then
            do j = 2*i, 100000, i
                p(j) = 1
            end do
        end if
    end do

    a = 0
    do i = 3, 100000
        if(p(i) == 0 .and. p((i+1)/2) == 0) then
            a(i) = a(i-1) + 1
        else
            a(i) = a(i-1)
        end if
    end do
    
    read(*,*) Q
    do i = 1, Q
        read(*,*) l, r
        write(*,*) a(r) - a(l-1)
    end do
    stop
end program