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 Rust (1.15.1) (judge verdict: Accepted)

use std::str::FromStr;
use std::io::*;

fn main() {
    let i = stdin();
    let o = stdout();
    run(&mut i.lock(), &mut o.lock());
}

fn run(i: &mut BufRead, o: &mut Write) {
    let hwd = read_vec::<usize>(i);
    let (h, w, d) = (hwd[0], hwd[1], hwd[2]);
    let wh = w * h;
    let mut a_to_xy = vec![(0, 0); wh + 1];
    for y in 0..h {
        let a = read_vec::<usize>(i);
        for x in 0..w {
            a_to_xy[a[x]] = (x, y);
        }
    }
    fn abs_sub(x0: usize, s1: usize) -> usize {
        (x0 as isize - s1 as isize).abs() as usize
    }

    let mut mps = vec![0; wh + 1];
    for i in 1..wh + 1 - d {
        let xy0 = a_to_xy[i];
        let xy1 = a_to_xy[i + d];
        mps[i + d] = mps[i] + abs_sub(xy0.0, xy1.0) + abs_sub(xy0.1, xy1.1);
    }

    let q = read::<usize>(i);
    for _ in 0..q {
        let lr = read_vec::<usize>(i);
        let (l, r) = (lr[0], lr[1]);
        let mp = mps[r] - mps[l];
        writeln!(o, "{}", mp).unwrap();
    }
}

fn read_line(i: &mut BufRead) -> String {
    let mut line = String::new();
    i.read_line(&mut line).unwrap();
    line.trim().to_string()
}

fn read<T: FromStr>(i: &mut BufRead) -> T {
    read_line(i).parse().ok().unwrap()
}
fn read_vec<T: FromStr>(i: &mut BufRead) -> Vec<T> {
    read_line(i)
        .split(' ')
        .map(|x| x.parse().ok().unwrap())
        .collect()
}