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: Time Limit Exceeded)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
	"strings"
)

type Point struct {
	x int
	y int
}

func main() {
	rdr := NewReader(100000)
	H, W, D := ScanInt(), ScanInt(), ScanInt()

	p := make(map[int]Point)
	for i := 0; i < H; i++ {
		s := ReadInts(rdr)
		for j, v := range s {
			p[v] = Point{i, j}
		}
	}

	memo := make([]int, H*W+1)
	for i := 1 + D; i <= H*W; i++ {
		p1, p2 := p[i-D], p[i]
		memo[i] = memo[i-D] + Abs(p1.x-p2.x) + Abs(p1.y-p2.y)
	}

	Q := ReadInt(rdr)

	for i := 0; i < Q; i++ {
		ints := ReadInts(rdr)
		L, R := ints[0], ints[1]
		fmt.Println(memo[R] - memo[L])
	}
}

type Reader struct {
	rdr  *bufio.Reader
	size int
}

func NewReader(size int) *Reader {
	return &Reader{
		bufio.NewReaderSize(os.Stdin, size),
		size,
	}
}

func ScanInt() (i int) {
	fmt.Scan(&i)
	return
}

func ReadLine(r *Reader) string {
	buf := make([]byte, 0, r.size)
	for {
		line, isPrefix, err := r.rdr.ReadLine()
		if err != nil {
			panic(err)
		}
		buf = append(buf, line...)
		if !isPrefix {
			break
		}
	}
	return string(buf)
}

func ReadStrs(r *Reader) []string {
	return strings.Split(ReadLine(r), " ")
}

func ReadInts(r *Reader) []int {
	a := ReadStrs(r)
	n := make([]int, 0)
	for _, v := range a {
		if i, e := strconv.Atoi(v); e == nil {
			n = append(n, i)
		}
	}
	return n
}

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

func ReadInt(r *Reader) (n int) {
	if i, e := strconv.Atoi(ReadLine(r)); e == nil {
		n = i
	}
	return
}