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 Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

import java.awt.Point
import java.util.*

fun main(args: Array<String>) {
    val sc = Scanner(System.`in`)

    val intArray = toIntArray(sc.nextLine())
    val h = intArray[0]
    val w = intArray[1]
    val d = intArray[2]

    val map = HashMap<Int, Point>()

    for (i in 0 until h) {
        val row = toIntArray(sc.nextLine())
        row.forEachIndexed { c, v ->
            map.put(v, Point(c, i))
        }
    }
    val memoMap = HashMap<String, Int>()
    val q = sc.nextLine().toInt()
    for (i in 0 until q) {
        val test = sc.nextLine()
        if (memoMap.containsKey(test)) {
            println(memoMap.get(test))
        } else {
            val testArray = toIntArray(test)
            var current = testArray[0]
            val end = testArray[1]
            var cur = map.get(current)
            var consumed = 0
            while (current <= end) {
                val next = map.get(current)
                if (cur != null && next != null) {
                    consumed += Math.abs(cur.x - next.x) + Math.abs(cur.y - next.y)
                }
                cur = next
                current += d
            }
            println(consumed)
            memoMap.put(test, consumed)
        }
    }
}

fun toIntArray(string: String): IntArray {
    val array = string.split(" ")
    val intArray = IntArray(array.size)
    array.forEachIndexed { i, s ->
        intArray[i] = Integer.parseInt(s)
    }
    return intArray
}