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)

#[allow(unused_imports)]
use std::io::*;
#[allow(unused_imports)]
use std::str::*;
#[allow(unused_imports)]
use std::mem::*;
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::HashMap;
#[allow(unused_imports)]
use std::collections::VecDeque;
#[allow(unused_imports)]
use std::usize;

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let mut line = String::new();
    stdin().read_line(&mut line).unwrap();
    line.trim().to_string().parse().ok().unwrap()
}

#[allow(dead_code)]
fn read_cols<T: FromStr>() -> Vec<T> {
    let mut line = String::new();
    stdin().read_line(&mut line).unwrap();

    line.trim()
        .split_whitespace()
        .map(|s| s.parse().ok().unwrap())
        .collect()
}

fn main() {
    let headers = read_cols::<u64>();
    let h = headers[0];
    let w = headers[1];
    let d = headers[2];

    let mut cell_indexes = Vec::<(i64, i64)>::new();
    cell_indexes.resize((h * w + 1) as usize, (-1, -1));
    for i in 0..h {
        let col = read_cols::<u64>();
        for j in 0..w {
            let n = col[j as usize];
            cell_indexes[n as usize] = (i as i64, j as i64);
        }
    }

    let mut jump_powers = Vec::<i64>::new();
    jump_powers.resize((h * w + 1) as usize, 0);
    for r in 1..d+1 {
        let mut sum = 0;

        let start = cell_indexes[r as usize];
        let mut current = start;
        for i in 1.. {
            let n = r + i * d;
            if n > h * w {
                break;
            }

            let next = cell_indexes[n as usize];
            sum += (current.0 - next.0).abs() + (current.1 - next.1).abs();
            jump_powers[n as usize] = sum;
            current = next;
        }
    }

    let num_queries = read::<u64>();
    for _ in 0..num_queries {
        let headers = read_cols::<usize>();
        let l = headers[0];
        let r = headers[1];

        let power = jump_powers[r] - jump_powers[l];

        println!("{}", power);
    }
}