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 Kotlin (1.0.0) (judge verdict: Runtime Error)

import java.io.PrintWriter

fun main(args: Array<String>) {

    // Sieve of Eratosthenes
    fun sieve(n: Int): Set<Int> {
        val primeNumbers = mutableSetOf<Int>()
        val sieved = mutableSetOf<Int>()

        for (i in 2..n) {
            if (sieved.contains(i)) continue
            primeNumbers.add(i)
            if (i * i <= n) {
                var j = 2
                while (i * j <= n) {
                    sieved.add(i * j)
                    j++
                }
            }
        }
        return primeNumbers
    }

    val primeNums = sieve(10000)
    val ans = IntArray(10001)
    for (i in 1..10000) {
        if (primeNums.contains(i) && primeNums.contains((i + 1) / 2)) {
            ans[i] = ans[i - 1] + 1
        } else {
            ans[i] = ans[i - 1]
        }
    }

    // main
    val pw = PrintWriter(System.out)

    val q = readLine()!!.toInt()
    repeat(q) {
        val (l, r) = readLine()!!.split(' ').map { it.toInt() }
        pw.println(ans[r] - ans[l - 1])
    }

    pw.flush()
}