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 PHP (5.6.30) (judge verdict: Time Limit Exceeded)

<?php
//error_reporting(0);
//$A = explode(" ",trim(fgets(STDIN)));
$Q = trim(fgets(STDIN));
//list($A,$B) = explode(" ",trim(fgets(STDIN)));
$cache=array();
for($i=0;$i<$Q;$i++) {
  $l[]=explode(" ",trim(fgets(STDIN)));
}
for($i=0;$i<$Q;$i++) {
  $r = 0;
  for($j=$l[$i][0];$j<=$l[$i][1];$j=$j+2) {
    if (isset($cache[$j]) && $cache[$j]==true) {
      $r++;
      continue;
    }
    $res = is2017($j);
    $cache[$j]=$res;
    if ($res) {
      $r++;
    }
  }
  printf("%d\n",$r);
}

function is2017($x) {
  global $cache;
  if (isPrime($x) && isPrime(($x+1)/2)) return true;
  return false;
}
function isPrime($x) {
    if ($x == 1) return False;
    $bCheck = True;
    $highestIntegralSquareRoot = floor(sqrt($x));
    for ($i = 2; $i <= $highestIntegralSquareRoot; $i++)
    {
        if ($x % $i == 0)
        {
             $bCheck = False;
             break;
        }
    }
    return $bCheck;
}