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>) {
    val Q = readLine()!!.toInt()
    var query = Array(Q, {arrayOf(0, 0)})
    var vmax = 0
    for (i in 0..Q-1) {
        var (low, high) = readLine()!!.split(" ").map{it.toInt()}
        if (high>vmax) vmax = high
        query[i][0] = low
        query[i][1] = high
    }
    // generate prime numbers
    var ref = Array(vmax+1, {true})
    ref[0] = false
    ref[1] = false
    for (i in 2..vmax/2) {
        if (ref[i]==false) continue
        for (j in 2..(vmax)/i) {
            ref[i*j] = false
        }
    }
    // check
    var ans = Array(vmax+1, {0})
    for (i in 1..vmax) {
        if (ref[i]&&ref[(i+1)/2]) ans[i] = ans[i-1]+1
        else ans[i] = ans[i-1]
    }
    query.forEach {
        println(ans[it[1]]-ans[it[0]-1])
    }
}