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 (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports)]
use proconio::{
   fastout, input,
   marker::{Bytes, Isize1, Usize1},
};

#[fastout]
fn main() {
   input! {
      h: usize,
      w: usize,
      d: usize,
      a: [[Usize1; w]; h],
      q: usize,
      lr: [(Usize1, Usize1); q]
   }
   let mut map = std::collections::BTreeMap::new();
   for i in 0..h {
      for j in 0..w {
         map.insert(a[i][j], (i as i32, j as i32));
      }
   }
   let mut mag = vec![vec![]; d];
   let mag_dif = |(x1, y1): (i32, i32), (x2, y2): (i32, i32)| (x1 - x2).abs() + (y1 - y2).abs();
   for i in 0..d {
      mag[i].push(0);
      let mut j = 1;
      while i + d * j < h * w {
         let x = mag[i][j - 1] + mag_dif(map[&(i + d * (j - 1))], map[&(i + d * j)]);
         mag[i].push(x);
         j += 1;
      }
   }
   for (l, r) in lr {
      let i = l % d;
      println!("{}", mag[i][r / d] - mag[i][l / d]);
   }
}