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.