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)

#!/usr/bin/perl
#abc84_d.pl
#Mon Jan  8 20:13:06 2018
#

use warnings;
use strict;

my $q = <STDIN>;
chomp $q;

my $loopnum = $q;

my @l;
my @r;

while ($loopnum > 0){
	my $stdin = <STDIN>;
	chomp $stdin;
	my @temp = split(" ",$stdin);
	push (@l, $temp[0]);
	push (@r, $temp[1]);
	$loopnum--;
}

my %primehash;
$primehash{"1"} = 0;
$primehash{"2"} = 1;

while ($loopnum <= $#l){
	my $testnum = $l[$loopnum];
	my $answer = 0;
	while ($testnum <= $r[$loopnum]){
		if (&prime($testnum) && &prime(($testnum+1)/2)){
			$answer++;
		}
		$testnum = $testnum+2;
	}
	print $answer,"\n";
	$loopnum++;
}



sub prime{
	my $query = $_[0];
	if (exists($primehash{$query})){
		return $primehash{$query};
	}
	my $sqrtquery = int(sqrt($query));
	my $testnum = 2;
	while ($testnum <= $sqrtquery+1){
		if ($query % $testnum == 0){
			$primehash{$query} = 0;
			return 0;
		}
		$testnum++;
	}
	$primehash{$query} = 1;
	return 1;
}