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::vec::Vec;
use std::cmp::*;
use std::collections::BinaryHeap;
use std::cmp::Ordering;

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 main() {
  let (h, w, d) = {
    let v: Vec<usize> = read_vec();
    (v[0], v[1], v[2])
  };

  let mut dist = vec![(0, 0); h * w + 1];
  for i in 0..h {
    let v: Vec<usize> = read_vec();
    for (j, e) in v.into_iter().enumerate() {
      dist[e] = (i as i64 + 1, j as i64 + 1);
    }
  }

  let mut lr: Vec<(i64, i64)> = Vec::new();
  let q: usize = read();
  for _ in 0..q {
    let t: Vec<i64> = read_vec();
    lr.push((t[0], t[1]));
  }

  let mut costs = vec![vec![0; (h * w + d - 1) / d]; d];
  for (i, &posit) in dist.iter().enumerate() {
    if i + d < h * w + 1 {
      let (x, y) = decode(i, d);
      costs[x][y] = cost_calc(posit, dist[i + d]);
    }
  }
  let mut sums_costs = vec![vec![0; (h * w + d - 1) / d + 1]; d];

  for (i, line) in costs.iter().enumerate() {
    for (j, &val) in line.iter().enumerate() {
      sums_costs[i][j+1] = sums_costs[i][j] + costs[i][j];
    }
  }
  for (l, r) in lr {
    let (i, j) = decode(l as usize, d);
    let (a, b) = decode(r as usize, d);
    println!("{}", sums_costs[a][b] - sums_costs[i][j]);
  }
}

fn cost_calc(x: (i64, i64), y: (i64, i64)) -> i64 {
  (x.0 - y.0).abs() + (x.1 - y.1).abs()
}

fn decode(x: usize, d: usize) -> (usize, usize) { (x % d, x / d) }

fn encode(i: usize, j: usize, d: usize) -> usize  { d * i + j }