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)

import java.util.Scanner

import scala.collection.mutable

object MathAlgo {
  def Primes(size: Int): Array[Int] = {
    var primes = new Array[Int](0)
    val flag = Array.fill[Boolean](size)(true)
    val limit = Math.sqrt(size).toInt

    (2 until limit).foreach(i => {
      if (flag(i)) {
        primes = primes :+ i
        (i until size by i).foreach(j => {
          flag(j) = false
        })
      }
    })

    (limit until size).foreach(i => {
      if (flag(i)) {
        primes = primes :+ i
      }
    })

    primes
  }
}

object Main {
  def main(args: Array[String]): Unit = {
    val sc = new Scanner(System.in)
    val P: Set[Int] = MathAlgo.Primes(200002).toSet
    var l2017nums: mutable.HashSet[Int] = new mutable.HashSet[Int]

    P.foreach(p => {
      if (P.contains((p+1)/2)) {
        l2017nums = l2017nums + p
      }
    })

    val Q = sc.nextInt
    (1 to Q).foreach(i => {
      var ans = 0
      val l, r = sc.nextInt
      (l to r).foreach(j => {
        if (l2017nums.contains(j)) {
          ans += 1
        }
      })

      println(ans)
    })
  }
}