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: Accepted)

import java.io.{BufferedReader, InputStream, InputStreamReader, PrintWriter}
import java.util.{Comparator, StringTokenizer}

import scala.collection.mutable
import scala.util.Sorting
import math.{abs, max, min}
import scala.collection.mutable.{ArrayBuffer, ListBuffer}

object Main {
  val MOD = 1000000007
  val out = new PrintWriter(System.out)
  def solve(): Unit = {
    val sc = new InputReader(System.in)
    val Q = sc.nextInt()

    val N = 100000
    val p = Array.ofDim[Int](N + 1)
    val d = Array.ofDim[Int](N + 1)

    (2 to math.sqrt(N).toInt) foreach { i =>
      if (p(i) == 0) {
        (2 to N / i) foreach { j =>
          p(j * i) = 1
        }
      }
    }

    (3 to N).reverse foreach { i =>
      if (p(i) == 0 && p((i + 1) / 2) == 0) d(i) = 1
    }

    (0 until N) foreach { i =>
      d(i + 1) += d(i)
    }

    (0 until Q) foreach { _ =>
      val l, r = sc.nextInt()
      out.println(d(r) - d(l - 1))
    }
  }


  def main(args: Array[String]): Unit = {
    solve()
    out.flush()
  }


  class InputReader(val stream: InputStream) {
    private val reader = new BufferedReader(new InputStreamReader(stream), 32768)
    private var tokenizer: StringTokenizer = null

    def next: String = {
      while (tokenizer == null || !tokenizer.hasMoreTokens)
        tokenizer = new StringTokenizer(reader.readLine)
      tokenizer.nextToken
    }

    def nextInt(): Int = next.toInt
    def nextLong(): Long = next.toLong
    def nextChar(): Char = next.charAt(0)
  }

}