Problem:
Score: 400 points

Problem Statement

In Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1, 2, 3, ..., N from west to east.
A company called AtCoder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i).
Takahashi the king is interested in the following Q matters:

The number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i \leq L_j and R_j \leq q_i.

Although he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.

Constraints

N is an integer between 1 and 500 (inclusive).

M is an integer between 1 and 200 \ 000 (inclusive).

Q is an integer between 1 and 100 \ 000 (inclusive).

1 \leq L_i \leq R_i \leq N (1 \leq i \leq M)

1 \leq p_i \leq q_i \leq N (1 \leq i \leq Q)

Input

Input is given from Standard Input in the following format:

N M Q
L_1 R_1
L_2 R_2
:
L_M R_M
p_1 q_1
p_2 q_2
:
p_Q q_Q

Output

Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.

Sample Input 1

2 3 1
1 1
1 2
2 2
1 2

Sample Output 1

3

As all the trains runs within the section from City 1 to City 2, the answer to the only query is 3.

Sample Input 2

10 3 2
1 5
2 8
7 10
1 7
3 10

Sample Output 2

1
1

The first query is on the section from City 1 to 7. There is only one train that runs strictly within that section: Train 1.
The second query is on the section from City 3 to 10. There is only one train that runs strictly within that section: Train 3.

Sample Input 3

10 10 10
1 6
2 9
4 5
4 7
4 7
5 8
6 6
6 7
7 9
10 10
1 8
1 9
1 10
2 8
2 9
2 10
3 8
3 9
3 10
1 10

Sample Output 3

7
9
10
6
8
9
6
7
8
10

Solution in Scala (2.11.7) (judge verdict: Wrong Answer)

import scala.collection.mutable

object Main {
  import io.StdIn._

  def getStrings = readLine().split(" ")
  def getInts = getStrings.map(_.toInt)

  def main(args: Array[String]): Unit = {
    val Array(n, m, q) = getInts
    type Interval = (Int, Int)
    val intervals: Seq[Interval] = (1 to m).map(_ => { val Array(l, r) = getInts; (l, r) })
    val queries: Seq[Interval] = (1 to q).map(_ => { val Array(l, r) = getInts; (l, r) })
    val intervalOpenCounts = Array.fill(n) { 0 }
    val intervalCloseCounts = Array.fill(n) { 0 }

    val superIntervalCounts = mutable.HashMap[Interval, Int]()
    (1 to n).foreach { l => (l to n).foreach { r => superIntervalCounts += (l, r) -> 0 } }

    for ((l, r) <- intervals) {
      (l + 1 until r).foreach(l1 => (l1 + 1 until r).foreach(r1 => {
        superIntervalCounts.update((l1, r1), superIntervalCounts((l1, r1)) + 1)
      }))
      intervalOpenCounts(l - 1) += 1
      intervalCloseCounts(r - 1) += 1
    }

    val intervalOpenScan = intervalOpenCounts.scan(0)(_ + _)
    val intervalCloseScan = intervalCloseCounts.scan(0)(_ + _)

    for ((l, r) <- queries) {
      println(intervalCloseScan(r) - intervalOpenScan(l - 1) + superIntervalCounts((l, r)))
    }
  }
}