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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

my $cnt = <STDIN> - 0;
sub isprime {
    my $n = shift;
    if($n < 2) { return 0; }
    foreach(2 ... $n - 1) {
        if($n % $_ == 0) { return 0; }
    }
    return 1;
}
my $s = "";
foreach(1 ... $cnt) {
    my ($low, $high) = map { $_ - 0 } split / /,<STDIN>;
    my $c = 0;
    foreach my $num ($low ... $high) {
        if(isprime($num) && isprime(($num + 1) / 2)) { $c++; }
    }
    $s .= "$c\n";
}
print $s;