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 PHP (5.6.30) (judge verdict: Time Limit Exceeded)

<?php
  

fscanf(STDIN,"%d %d %d",$H,$W,$D);
$A = [];

for($i = 0; $i<$H; $i++){
  $A[$i] = explode(" ",trim(fgets(STDIN)));
}

fscanf(STDIN,"%d",$Q);

$L = [];
$R = [];
for($j = 0; $j < $Q; $j++){
  fscanf(STDIN, "%d %d", $L[$j], $R[$j]);
}


//Qがマックスになるまで試験を続ける
for($q = 0; $q<$Q; $q++){
  $magic_pow = 0;
  $origin = $L[$q];
  $dest = $R[$q];
  while($origin < $dest){
    $originHW = getHW($A,$origin,$H,$W);
    $destHW = getHW($A,$origin+$D,$H,$W);
    $origin += $D;
    $magic_pow += getDistance($originHW,$destHW);
  }
  echo "$magic_pow\n";
}



function getHW($A,$val,$H,$W){
  $hw = array("h" => null, "w" => null);
  for($i = 0; $i<$H; $i++){
    for($j = 0; $j<$W; $j++){
      if($A[$i][$j] == $val){
        $hw["h"] = $i;
        $hw["w"] = $j;
        return $hw;
      }
    }
  }
}


function getDistance($arr1,$arr2){
  return abs($arr1["h"]-$arr2["h"])+abs($arr1["w"]-$arr2["w"]);
}