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)]
#![allow(non_snake_case)]

use std::*;
use std::collections::*;
use std::ops::*;
use procon::*;

pub fn main() -> () {
    let (H, W, D) = {
        let xs = read_words::<usize>();
        (xs[0], xs[1], xs[2])
    };
    let mut A = make_vec(H, |_| make_vec(W, |_| 0));
    for y in 0..H {
        for (x, a) in read_words::<usize>().into_iter().enumerate() {
            A[y][x] = a - 1;
        }
    }

    let costs = {
        let HW = H * W;

        let distance =
            |(y1, x1): (i32, i32), (y2, x2): (i32, i32)| (y1 - y2).abs() + (x2 - x1).abs();

        let mut points = make_vec(HW, |_| (0, 0));
        for y in 0..H {
            for x in 0..W {
                points[A[y][x]] = (y as i32, x as i32);
            }
        }

        let mut costs = make_vec(HW, |_| 0i64);
        for i in 0..HW {
            costs[i] = if i < D {
                0
            } else {
                let d = distance(points[i], points[i - D]) as i64;
                costs[i - D] + d
            };
        }

        costs
    };

    let Q = read_line().parse::<usize>().unwrap();
    for _ in 0..Q {
        let (l, r) = {
            let xs = read_words::<usize>();
            (xs[0] - 1, xs[1] - 1)
        };
        let cost = costs[r] - costs[l];
        println!("{}", cost);
    }
    return;
}

pub mod procon {
    use std;
    use std::collections::*;
    use std::io;
    use std::mem;
    use std::str::FromStr;

    pub fn read_line() -> String {
        let mut buf = String::new();
        io::stdin().read_line(&mut buf).unwrap();
        buf.trim_right().to_owned()
    }

    pub fn read_words<T>() -> Vec<T>
    where
        T: std::str::FromStr,
        T::Err: std::fmt::Debug,
    {
        let mut buf = String::new();
        io::stdin().read_line(&mut buf).unwrap();
        buf.split_whitespace()
            .map(|word| T::from_str(word).unwrap())
            .collect()
    }

    pub fn read_vec(len: usize) -> Vec<String> {
        let mut vec = Vec::new();
        while vec.len() < len {
            let line = read_line();
            for word in line.split_whitespace() {
                vec.push(word.to_owned());
            }
        }
        assert!(vec.len() == len);
        vec
    }

    pub fn make_vec<T, F>(len: usize, f: F) -> Vec<T>
    where
        F: Fn(usize) -> T,
    {
        return (0..len).into_iter().map(f).collect();
    }
}