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 Go (1.6) (judge verdict: Wrong Answer)

package main

import "fmt"

var H, W, D int
var A [][]int
var Q int
var L, R []int

func main() {
	fmt.Scanf("%d %d %d", &H, &W, &D)

	A = make([][]int, H)
	for i := 0; i < H; i++ {
		A[i] = make([]int, W)
		for j := 0; j < W; j++ {
			fmt.Scanf("%d", &A[i][j])
		}
	}

	fmt.Scanf("%d", &Q)

	L = make([]int, Q)
	R = make([]int, Q)

	for i := 0; i < Q; i++ {
		fmt.Scanf("%d %d", &L[i], &R[i])
	}

	m := make(map[int]Point, H*W)
	for i := 0; i < H; i++ {
		for j := 0; j < W; j++ {
			m[A[i][j]] = Point{i, j}
		}
	}

	ans := make(map[int]map[int]int)
	for i := 1; i <= H*W; i++ {
		ans[i] = make(map[int]int)
	}

	for i := 0; i < Q; i++ {
		c := m[L[i]]
		for d := L[i]; d+D <= R[i]; d += D {
			if _, ok := ans[d][R[i]]; ok {
				break
			}
			n := m[d+D]
			dist := Abs(c.x-n.x) + Abs(c.y-n.y)
			for j := L[i]; j <= d; j += D {
				ans[j][d+D] = ans[j][d] + dist
			}
			c = n
		}
		fmt.Println(ans[L[i]][R[i]])
	}
}

func Abs(x int) int {
	if x < 0 {
		return -x
	}
	return x
}

type Point struct {
	x int
	y int
}