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)

use proconio::{fastout, input, marker::Usize1};
use std::collections::HashMap;

#[fastout]
fn main() {
    input! {
        h: usize,
        w: usize,
        d: usize,
        a: [[Usize1; w]; h],
        q: usize,
        lr: [(Usize1, Usize1); q],
    }

    let mut hm = HashMap::new();
    for i in 0..h {
        for j in 0..w {
            hm.insert(a[i][j], (i, j));
        }
    }
    let mut modulo = vec![vec![0i64]; d];
    for i in d..h * w {
        let pn = hm.get(&i).unwrap();
        let pb = hm.get(&(i - d)).unwrap();
        let dist = i64::abs(pb.0 as i64 - pn.0 as i64) + i64::abs(pb.1 as i64 - pn.1 as i64);
        let last = modulo[i % d][modulo[i % d].len() - 1];
        modulo[i % d].push(last + dist);
    }

    for i in 0..q {
        let l = lr[i].0;
        let r = lr[i].1;
        println!("{}", modulo[r % d][r / d] - modulo[l % d][l / d]);
    }
}