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)

fun main(args: Array<String>) {
    val (H, W, D) = readLine()!!.split(" ").map { it.toInt() }
    val A = mutableListOf<IntArray>()
    (1..H).forEach {
        val ai = readLine()!!.split(" ").map { it.toInt() }.toIntArray()
        A.add(ai)
    }
    // O(HW) Create function to retrieve the poistion of num N in O(1)
    val numToPosition = Array(H * W + 1, { Pair(-1, -1) })
    (0 until H).forEach {h ->
        (0 until W).forEach {w ->
            val num = A[h][w]
            numToPosition[num] = Pair(h, w)
        }
    }
    fun getPositionByNumber(num: Int) : Pair<Int, Int> {
        return numToPosition[num]
    }

    val Q = readLine()!!.toInt()

    // Return cost
    fun useMagic(i: Int, j: Int, x: Int, y: Int) : Int {
        return Math.abs(x - i) + Math.abs(y - j)
    }

    // O(Q)
    (1..Q).forEach {
        var cost = 0L
        val (L, R) = readLine()!!.split(" ").map { it.toInt() }
        var x = L
        // R - L = DX // R = DX + L
        // O((R-L)/D) (<= O(HW)) // TODO should be faster, could be written in graph
        while (x != R) {
            var next = x + D
            val (currentX, currentY) = getPositionByNumber(x)
            val (nextX, nextY) = getPositionByNumber(next)
            cost += useMagic(currentX, currentY, nextX, nextY)
            x = next
        }
        println(cost)
    }
}