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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)

object Main extends App {
  val scanner = new java.util.Scanner(System.in)

  val q = scanner.nextInt()

  val queries = (1 to q).map { _ =>
    (scanner.nextInt(), scanner.nextInt())
  }

  def prims(n: Int): Seq[Int] = {
    def sieve(xs: Seq[Int]): Seq[Int] = xs match {
      case Nil   => Nil
      case x+:xs => x +: sieve(xs.filter(_ % x != 0))
    }

    sieve((2 to n))
  }

  val max = queries.foldLeft(0) { (m, q) =>
    if(q._2 > m) q._2 else m
  }

  queries.map {
    case (l, r) =>
      val nums = l to r
      val ps = prims(r).toSeq
      nums.filter(n => ps.contains(n) && ps.contains((n+1)/2)).size
  }.foreach(println)
}