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(non_snake_case)]

use std::io::{stdin, Read};
use std::str::FromStr;
fn read_option<T: FromStr>() -> Option<T> {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok()
}
fn read<T: FromStr>() -> T {
    let opt = read_option();
    opt.expect("failed to parse token")
}

fn main() {
    let H: usize = read();
    let W: usize = read();
    let D: usize = read();
    let mut board: Vec<Vec<usize>> = vec![];
    for _ in 0..H {
        let mut vec: Vec<usize> = vec![];
        for _ in 0..W {
            let v = read::<usize>() - 1;
            vec.push(v);
        }
        board.push(vec);
    }
    let Q: usize = read();
    let queries: Vec<(usize, usize)> = (0..Q)
        .map(|_| (read::<usize>() - 1, read::<usize>() - 1))
        .collect();
    let ans = solve(D, &board, &queries);
    println!(
        "{}",
        ans.iter()
            .map(|i| i.to_string())
            .collect::<Vec<_>>()
            .join("\n")
    );
}

fn solve(d: usize, board: &[Vec<usize>], queries: &[(usize, usize)]) -> Vec<usize> {
    let mut rev_board: Vec<(usize, usize)> = vec![(0, 0); board.len() * board[0].len()];
    for (i, row) in board.iter().enumerate() {
        for (j, &v) in row.iter().enumerate() {
            rev_board[v] = (i, j);
        }
    }
    let mut scores = vec![vec![0]; d];
    for i in d..rev_board.len() {
        let rem = i % d;
        let before = rev_board[i - d];
        let now = rev_board[i];
        let score = (before.0 as isize - now.0 as isize).abs() as usize
            + (before.1 as isize - now.1 as isize).abs() as usize;
        let last = scores[rem].last().unwrap().clone();
        scores[rem].push(score + last);
    }
    queries
        .iter()
        .map(|&(start, end)| {
            let rem = start % d;
            scores[rem][end / d] - scores[rem][start / d]
        })
        .collect()
}