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: Accepted)

fun main(args: Array<String>) {
    val sc = java.util.Scanner(System.`in`)
    val h = sc.nextInt()
    val w = sc.nextInt()
    val d = sc.nextInt()

    data class Pos(val x: Int, val y: Int, var dsum: Int = 0)

    val A: Array<Array<Pos>> = Array(d) { Array(h * w / d + 1) { Pos(9999, 9999) } }

    for (y in 0 until h) {
        for (x in 0 until w) {
            val v = sc.nextInt() - 1 // to 0 origin
            A[v % d][v / d] = Pos(x, y)
        }
    }
    for (di in 0 until d) {
        var dsum = 0
        if (A[di].isNotEmpty()) {
            var t = A[di][0]
            for (i in 1 until A[di].count()) {
                val tnext = A[di][i]
                dsum += Math.abs(t.x - tnext.x) + Math.abs(t.y - tnext.y)
                tnext.dsum = dsum
                t = tnext
            }
        }
    }

    val q = sc.nextInt()
    for (i in 0 until q) {
        var m = 0
        val L = sc.nextInt() - 1
        val R = sc.nextInt() - 1

        val Ld = A[L % d][L / d].dsum
        val Rd = A[R % d][R / d].dsum

        println(Rd - Ld)
    }
}