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 PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php
fscanf(STDIN, '%d', $Q);
$query = array();
$subQuery = array();
for($i = 0; $i < $Q; $i++) {
	fscanf(STDIN, "%d %d", $l, $r);
	array_push($subQuery, $l);
	array_push($subQuery, $r);
	array_push($query, $subQuery);
	$subQuery= array();
}

$ans = array();
for ($i = 0; $i < $Q; $i++) {
	$count = 0;
	for ($k = ($query[$i][0]-1)/2; $k <= ($query[$i][1]-1)/2; $k++) {
		$big = 2*$k+1;
		$small = ((2*$k+1)+1)/2;
		
		$primeFlag = true;
		for ($j = 3; $j < $big; $j+=2) {
			if ($small % $j === 0 && $j < $small) {
				$primeFlag = false;
			} else if ($big % $j === 0 && $j < $big) {
				$primeFlag = false;
			} else if (($big % 2 === 0 && $big > 2) || ($small % 2 === 0 && $small > 2)) {
				$primeFlag = false;
			}
		}
		
		if ($primeFlag === true && $small !== 1) {
			$count++;
		}
	}

	array_push($ans, $count);
}

foreach ($ans as $num) {
	echo $num.PHP_EOL;
}