100893: [AtCoder]ABC089 D - Practical Skill Test

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