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);

for ( $i = 0; $i < $H; $i++) {
    $S = explode(' ', trim(fgets(STDIN)));

    for($j = 0; $j < $W; $j++){
        $A[$i][$j] = $S[$j];    //[行][列]
    }
}

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

for ( $k = 0; $k < $Q; $k++) {
    fscanf(STDIN, "%d %d", $L, $R);

    $maryoku = 0;
    $x = $L;

    $flag = 0;
    for( $i = 0; $i < $H; $i++){
        for($j = 0; $j < $W; $j++){
            if($A[$i][$j] == $x){
                $I1 = $i;
                $J1 = $j;
                $flag = 1;
                break;
            }
        }
        if($flag == 1){
            break;
        }
    }

    while(1){
        $x = $x + $D;
        if($x > $R){
            break;
        }

        $flag = 0;
        for( $i = 0; $i < $H; $i++){
            for($j = 0; $j < $W; $j++){
                if($A[$i][$j] == $x){
                    $I2 = $i;
                    $J2 = $j;
                    $flag = 1;
                    break;
                }
            }
            if($flag == 1){
                break;
            }
        }

        $maryoku += abs($I1 - $I2) + abs($J1 - $J2);

        $I1 = $I2;
        $J1 = $J2;
    }

    out::println($maryoku);

}


class out {
    public static function println($str = "") {
        echo $str . PHP_EOL;
    }
}

?>