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: Accepted)

$Q = <STDIN>;chomp $Q;
@P=(2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317);
$s=0;
for($i=3;$i<=100000;$i++){
	$f=1;
	$ii=($i+1)/2;
	for($j=0;$P[$j]*$P[$j]<=$ii;$j++){
		if($ii%$P[$j]==0) { $f=0; last; }
	}
	if ($f) {
		for($j=0;$P[$j]*$P[$j]<=$i;$j++){
			if($i%$P[$j]==0) { $f=0; last;}
		}
		$s=$s+1 if ($f);
	}
	$S[$i]=$s;
}
for($i=$Q;$i>0;$i--){
	($l,$r)=split " ",<STDIN>;
	$c=$S[$r]-$S[$l-1];
	print "$c\n";
}