Problem:
Score : 400 points

Problem Statement

We have a grid with H rows and W columns. The square at the i-th row and the j-th column will be called Square (i,j).

The integers from 1 through H×W are written throughout the grid, and the integer written in Square (i,j) is A_{i,j}.

You, a magical girl, can teleport a piece placed on Square (i,j) to Square (x,y) by consuming |x-i|+|y-j| magic points.

You now have to take Q practical tests of your ability as a magical girl.

The i-th test will be conducted as follows:

Initially, a piece is placed on the square where the integer L_i is written.

Let x be the integer written in the square occupied by the piece. Repeatedly move the piece to the square where the integer x+D is written, as long as x is not R_i. The test ends when x=R_i.

Here, it is guaranteed that R_i-L_i is a multiple of D.

For each test, find the sum of magic points consumed during that test.

Constraints

1 \leq H,W \leq 300

1 \leq D \leq H×W

1 \leq A_{i,j} \leq H×W

A_{i,j} \neq A_{x,y} ((i,j) \neq (x,y))

1 \leq Q \leq 10^5

1 \leq L_i \leq R_i \leq H×W

(R_i-L_i) is a multiple of D.

Input

Input is given from Standard Input in the following format:

H W D
A_{1,1} A_{1,2} ... A_{1,W}
:
A_{H,1} A_{H,2} ... A_{H,W}
Q
L_1 R_1
:
L_Q R_Q

Output

For each test, print the sum of magic points consumed during that test.

Output should be in the order the tests are conducted.

Sample Input 1

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

Sample Output 1

5

4 is written in Square (1,2).

6 is written in Square (3,3).

8 is written in Square (3,1).

Thus, the sum of magic points consumed during the first test is (|3-1|+|3-2|)+(|3-3|+|1-3|)=5.

Sample Input 2

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

Sample Output 2

0
0

Note that there may be a test where the piece is not moved at all, and there may be multiple identical tests.

Sample Input 3

5 5 4
13 25 7 15 17
16 22 20 2 9
14 11 12 1 19
10 6 23 8 18
3 21 5 24 4
3
13 13
2 10
13 13

Sample Output 3

0
5
0

Solution in Scala (2.11.7) (judge verdict: Accepted)

import java.io.{BufferedReader, IOException, InputStream, InputStreamReader}
import java.util.{Scanner, StringTokenizer}

import scala.util.Sorting

object Main {
  def solve(): Unit = {
    val sc = new InputReader(System.in)
    val H = sc.nextInt()
    val W = sc.nextInt()
    val D = sc.nextInt()
    val N = H * W
    val A = Array.ofDim[(Int, Int)](N + 1)
    
    for {
      h <- 1 to H
      w <- 1 to W
    } {
      val x = sc.nextInt()
      A(x) = (h, w)
    }

    def move(s: (Int, Int), t: (Int, Int)) = math.abs(s._1 - t._1) + math.abs(s._2 - t._2)

    // (1 to D-1) から xまでのコスト
    val cost = Array.ofDim[Int](N + 1)
    (1 to D) foreach { d =>  // 最初の地点dから
      (0 until (N / D) + (if(d <= N % D) 1 else 0)) foreach { j =>  // j回移動する
        if (j == 0) cost(d) = 0
        else {
          val next = d + D * j
          val prev = d + D * (j - 1)
          cost(next) = cost(prev) + move(A(prev), A(next))
        }
      }
    }

    val Q = sc.nextInt()
    (0 until Q) foreach { _ =>
      val L = sc.nextInt()
      val R = sc.nextInt()
      println(cost(R) - cost(L))
    }
  }

  def main(args: Array[String]): Unit = {
    solve()
  }

  class InputReader(val stream: InputStream) {
    val reader = new BufferedReader(new InputStreamReader(stream), 32768)
    var tokenizer: StringTokenizer = null

    def next: String = {
      while (tokenizer == null || !tokenizer.hasMoreTokens)
        tokenizer = new StringTokenizer(reader.readLine)
      tokenizer.nextToken
    }

    def nextInt(): Int = next.toInt
  }
}