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: Accepted)

fun main(args: Array<String>) {
    fun getPrimeListByEratosthenes(maxValue: Int): BooleanArray {
        val isPrime = BooleanArray(maxValue + 1) { true }
        isPrime[0] = false
        isPrime[1] = false
        val root = Math.sqrt(maxValue.toDouble()).toInt() + 1
        for (i in 2..root) {
            if (isPrime[i]) {
                var j = i * 2
                while (j < maxValue) {
                    isPrime[j] = false
                    j += i
                }
            }
        }
        return isPrime
    }

    val q = readLine()!!.toInt()
    val maxValue = 100000
    val isPrime = getPrimeListByEratosthenes(maxValue)
    val spCount = IntArray(maxValue + 1) { 0 }
    (1..maxValue).forEach { spCount[it] = spCount[it - 1] + if (it % 2 == 1 && isPrime[it] && isPrime[(it + 1) / 2]) 1 else 0 }
    (1..q).forEach {
        val (l, r) = readLine()!!.split(' ').map(String::toInt)
        println(spCount[r] - spCount[l - 1])
    }
}