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: Accepted)

package main

import (
	"bufio"
	"bytes"
	"fmt"
	"io"
	"os"
	"strconv"
)

func main() {
	defer Flush()

	H := readi()
	W := readi()
	D := readi()
	A := make([][]int, H)
	for i := range A {
		A[i] = make([]int, W)
		for j := range A[i] {
			A[i][j] = readi()
		}
	}
	Q := readi()
	L := make([]int, Q)
	R := make([]int, Q)
	for i := range L {
		L[i] = readi()
		R[i] = readi()
	}

	p := make([][2]int, H*W+D+1)
	for i := range A {
		for j := range A[i] {
			c := A[i][j]
			p[c][0] = i
			p[c][1] = j
		}
	}
	s := make([]int, len(p)+2*D+1)
	for i := 0; i <= H*W; i++ {
		x := abs(p[i][0] - p[i+D][0])
		y := abs(p[i][1] - p[i+D][1])
		z := s[i] + x + y
		s[i+D] = z
	}

	for i := range L {
		l, r := L[i], R[i]
		println(s[r] - s[l])
	}
}

// -----------------------------------------------------------------------------

// IO helper functions

// Returns next token from input.  It must be initialized by SetInput()
// before the first call.
var nextToken func() ([]byte, error)
var nextLine func() ([]byte, error)

// Holds a buffer for output.  It must be initialized by SetOutput().
// All IO fucntions (read*() and [e]print*()) should write to OutputWriter
// instead of this.
var OutputBuffer *bufio.Writer

// Holds an io.Writer.  It must be initialized by SetOutput()
var OutputWriter io.Writer

// Set IO functions for interactive input/output.
func SetInteractive(w io.Writer, r io.Reader) {
	SetUnbefferedInput(r)
	OutputBuffer = nil
	OutputWriter = w
}

// Setup OutputBuffer and OutputWriter.
func SetOutput(w io.Writer) {
	OutputBuffer = bufio.NewWriter(w)
	OutputWriter = OutputBuffer
}

// Flushes OutputBuffer
func Flush() {
	if OutputBuffer != nil {
		OutputBuffer.Flush()
	}
}

// Returns true if c is a white space
func IsSpace(c byte) bool {
	switch c {
	case '\t', '\n', '\v', '\f', '\r', ' ':
		return true
	}
	return false
}

func IsNewLine(c byte) bool {
	switch c {
	case '\n', '\r':
		return true
	}
	return false
}

// Setup nextToken with input buffer.
func SetInput(r io.Reader) {
	buf := new(bytes.Buffer)
	var b []byte

	var i int
	rest := func() ([]byte, error) {
		for i < len(b) && IsSpace(b[i]) {
			i++
		}
		if i == len(b) {
			return nil, io.ErrUnexpectedEOF
		}
		j := i
		for i < len(b) && !IsSpace(b[i]) {
			i++
		}
		return b[j:i], nil
	}
	initial := func() ([]byte, error) {
		io.Copy(buf, r)
		b = buf.Bytes()
		nextToken = rest
		return rest()
	}
	nextToken = initial

	restLn := func() ([]byte, error) {
		for i < len(b) && IsNewLine(b[i]) {
			i++
		}
		if i == len(b) {
			return nil, io.ErrUnexpectedEOF
		}
		j := i
		for i < len(b) && !IsNewLine(b[i]) {
			i++
		}
		return b[j:i], nil
	}

	initialLn := func() ([]byte, error) {
		io.Copy(buf, r)
		b = buf.Bytes()
		nextLine = restLn
		return restLn()
	}
	nextLine = initialLn
}

// Setup nextToken without input buffer.
func SetUnbefferedInput(r io.Reader) {
	buf := bufio.NewReader(r)
	var b []byte

	var i int
	nextToken = func() ([]byte, error) {
		var err error
		if i == len(b) {
			b, err = buf.ReadBytes('\n')
			if err != nil {
				return nil, err
			}
			i = 0
			j := len(b) - 1
			for 0 <= j && IsSpace(b[j]) {
				j--
			}
			b = b[0 : j+1]
		}
		for i < len(b) && IsSpace(b[i]) {
			i++
		}
		j := i
		for i < len(b) && !IsSpace(b[i]) {
			i++
		}
		if i == j {
			return nil, io.ErrUnexpectedEOF
		}
		return b[j:i], nil
	}
}

// -----------------------------------------------------------------------------

// IO functions

// Reads next token and return it as []byte
func readb() []byte {
	b, err := nextToken()
	if err != nil {
		panic(err)
	}
	return b[:len(b):len(b)]
}

// Reads next token and return it as string
func reads() string {
	return string(readb())
}

// Read next line as []byte.  Trailing '\n' will not be included.
// See also comments on readb()
func readbln() []byte {
	b, err := nextLine()
	if err != nil {
		panic(err)
	}
	return b[:len(b):len(b)]
}

// Read next line as string
func readsln() string {
	return string(readbln())
}

// Reads next token and return it as int64
func readll() int64 {
	i, err := strconv.ParseInt(reads(), 10, 64)
	if err != nil {
		panic(err.Error())
	}
	return i
}

// Reads next token and return it as int
func readi() int {
	return int(readll())
}

// Reads next token and return it as float64
func readf() float64 {
	f, err := strconv.ParseFloat(reads(), 64)
	if err != nil {
		panic(err.Error())
	}
	return f
}

// Write args to OutputWriter with the format f
func printf(f string, args ...interface{}) (int, error) {
	return fmt.Fprintf(OutputWriter, f, args...)
}

// Write args to OutputWriter without format
func println(args ...interface{}) (int, error) {
	return fmt.Fprintln(OutputWriter, args...)
}

// Write args to stderr with the format f
func eprintf(f string, args ...interface{}) (int, error) {
	return fmt.Fprintf(os.Stderr, f, args...)
}

// Write args to stderr without format
func eprintln(args ...interface{}) (int, error) {
	return fmt.Fprintln(os.Stderr, args...)
}

// -----------------------------------------------------------------------------

// Utilities

func sumSlice(a []int) int {
	var res int
	for _, v := range a {
		res += v
	}
	return res
}

func sumSlicell(a []int64) int64 {
	var res int64
	for _, v := range a {
		res += v
	}
	return res
}

func readInts(N int) (int, []int) {
	if N == 0 {
		N = readi()
	}
	a := make([]int, N)
	for i := range a {
		a[i] = readi()
	}
	return N, a
}

func readIntsll(N int) (int, []int64) {
	if N == 0 {
		N = readi()
	}
	a := make([]int64, N)
	for i := range a {
		a[i] = readll()
	}
	return N, a
}

// reverse slice in place
func reverse(a []int) {
	for i, j := 0, len(a)-1; i < j; i, j = i+1, j-1 {
		a[i], a[j] = a[j], a[i]
	}
}

// areverse: allocating reverse
func areverse(a []int) []int {
	b := make([]int, len(a))
	for i := range a {
		b[i] = a[len(a)-i-1]
	}
	return b
}

// -----------------------------------------------------------------------------

// Simple math functions

const (
	// big prime
	INF  = 1000000007
	INF2 = 1000000009
	INF3 = 998244353
)

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func minll(a, b int64) int64 {
	if a < b {
		return a
	}
	return b
}

func minf(a, b float64) float64 {
	if a < b {
		return a
	}
	return b
}

func max(a, b int) int {
	if a < b {
		return b
	}
	return a
}

func maxll(a, b int64) int64 {
	if a < b {
		return b
	}
	return a
}

func maxf(a, b float64) float64 {
	if a < b {
		return b
	}
	return a
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

func absll(a int64) int64 {
	if a < 0 {
		return -a
	}
	return a
}

func absf(a float64) float64 {
	if a < 0 {
		return -a
	}
	return a
}

// egcd(a, b) returns d, x, y:
//   d is gcd(a,b)
//   x, y are  integers that satisfy ax + by = d
func egcd(a, b int) (int, int, int) {
	if b == 0 {
		return a, 1, 0
	}
	d, x, y := egcd(b, a%b)
	return d, y, x - a/b*y
}

func egcdll(a, b int64) (int64, int64, int64) {
	if b == 0 {
		return a, 1, 0
	}
	d, x, y := egcdll(b, a%b)
	return d, y, x - a/b*y
}

func gcd(a, b int) int {
	d, _, _ := egcd(a, b)
	return d
}

func gcdll(a, b int64) int64 {
	d, _, _ := egcdll(a, b)
	return d
}

// set up IO functions
func init() {
	// for non-interactive
	SetInput(os.Stdin)
	SetOutput(os.Stdout)

	// Enable below when interactive.  Its ok to leave above intact.
	// SetInteractive(os.Stdout, os.Stdin)
}