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::collections::HashMap;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn manhattern_dist(p1: (usize, usize), p2: (usize, usize)) -> usize {
    let (x1, y1) = p1;
    let (x2, y2) = p2;
    ((x1 as i32- x2 as i32).abs() + (y1 as i32 - y2 as i32).abs()) as usize
}

fn main() {
    let v = read_vec::<usize>();
    let (h, w, d) = (v[0], v[1], v[2]);
    let mut grid: HashMap<usize, (usize, usize)> = HashMap::new();
    for i in 0..h {
        let v = read_vec::<usize>();
        for j in 0..w {
            grid.insert(v[j] - 1, (i, j));
        }
    }
    // println!("grid {:?}", grid);

    let query_size: usize = read();
    let mut queries = vec![(0, 0); query_size];
    for q_idx in 0..query_size {
        let v = read_vec::<usize>();
        queries[q_idx] = (v[0] - 1, v[1] - 1);
    }

    let mut sums = vec![vec![0; h * w / d + 1]; d];
    for i in 0..d {
        let mut search_num = i;
        let mut j = 0;
        while search_num + d < h * w {
            sums[i][j + 1] = sums[i][j] + manhattern_dist(grid[&search_num], grid[&(search_num + d)]);
            // println!("{:?}", (search_num, sums[i][j], grid[&search_num], grid[&(search_num + d)], manhattern_dist(grid[&search_num], grid[&(search_num + d)])));
            search_num += d;
            j += 1;
        }
    }
    // println!("sums {:?}", sums);

    for q in queries {
        let q = (q.0, q.1);
        let idx1 = q.0 % d;
        let start_idx2 = q.0 / d;
        let end_idx2 = q.1 / d;
        // println!("{:?}", (q, d, &sums[idx1], start_idx2, end_idx2));
        let ans = sums[idx1][end_idx2] - sums[idx1][start_idx2];
        println!("{:?}", ans);
    }
}