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(dead_code)]
fn main() {
    let (h, w, d) = i::u3();
    let mut a = Vec::new();
    for _ in 0..h {
        a.push(i::uv(w));
    }
    let q = i::u();
    let lr = i::uv2(q);

    let grid = Grid::new(h, w, a);
    let mut map = HashMap::new();
    for i in 0..(h * w) {
        let g = grid.get(i);
        map.insert(g, (grid.x(i), grid.y(i)));
    }

    let mut cost = vec![0; h * w + 1];
    for i in d + 1..(h * w + 1) {
        let (bx, by) = map[&i];
        let (ax, ay) = map[&(i - d)];
        cost[i] = cost[i - d] + max(ax, bx) - min(ax, bx) + max(ay, by) - min(ay, by);
    }

    for (l, r) in lr {
        println!("{}", cost[r] - cost[l]);
    }
}
#[allow(unused_imports)]
use grid::*;

#[allow(dead_code)]
mod grid {
    #[derive(Debug)]
    pub struct Grid<T> {
        pub h: usize,
        pub w: usize,
        pub max: usize,
        pub map: Vec<T>,
    }

    impl<T: Clone> Grid<T> {
        pub fn new(h: usize, w: usize, map: Vec<Vec<T>>) -> Grid<T> {
            let mut flat = Vec::new();
            for r in map {
                for c in r {
                    flat.push(c);
                }
            }
            Grid {
                h: h,
                w: w,
                max: h * w,
                map: flat,
            }
        }
        pub fn key(&self, x: usize, y: usize) -> usize {
            y * self.w + x
        }
        pub fn xy(&self, k: usize) -> (usize, usize) {
            (self.x(k), self.y(k))
        }
        pub fn x(&self, k: usize) -> usize {
            k % self.w
        }
        pub fn y(&self, k: usize) -> usize {
            k / self.w
        }
        pub fn get(&self, key: usize) -> &T {
            &self.map[key]
        }
        pub fn set(&mut self, key: usize, value: T) {
            self.map[key] = value;
        }
        pub fn neighbor(&self, key: usize) -> Vec<usize> {
            let mut ret = Vec::new();
            if self.x(key) + 1 < self.w {
                ret.push(key + 1);
            }
            if self.y(key) + 1 < self.h {
                ret.push(key + self.w);
            }
            if self.x(key) > 0 {
                ret.push(key - 1);
            }
            if self.y(key) > 0 {
                ret.push(key - self.w);
            }
            ret
        }
        pub fn one_way(&self, key: usize) -> Vec<usize> {
            let mut ret = Vec::new();
            if self.x(key) + 1 < self.w {
                ret.push(key + 1);
            }
            if self.y(key) + 1 < self.h {
                ret.push(key + self.w);
            }
            ret
        }
    }
}

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::{HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::io::*;
#[allow(unused_imports)]
use std::num::*;
#[allow(unused_imports)]
use std::str::*;

#[allow(dead_code)]
mod i {
    use super::*;

    pub fn read<T: FromStr>() -> T {
        stdin()
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>()
            .parse::<T>()
            .ok()
            .unwrap()
    }

    pub fn str() -> String {
        read()
    }

    pub fn s() -> Vec<char> {
        str().chars().collect()
    }

    pub fn i() -> i64 {
        read()
    }

    pub fn u() -> usize {
        read()
    }

    pub fn u2() -> (usize, usize) {
        (read(), read())
    }

    pub fn u3() -> (usize, usize, usize) {
        (read(), read(), read())
    }

    pub fn f() -> f64 {
        read()
    }

    pub fn c() -> char {
        read::<String>().pop().unwrap()
    }

    pub fn iv(n: usize) -> Vec<i64> {
        (0..n).map(|_| i()).collect()
    }

    pub fn iv2(n: usize) -> Vec<(i64, i64)> {
        (0..n).map(|_| iv(2)).map(|a| (a[0], a[1])).collect()
    }

    pub fn uv(n: usize) -> Vec<usize> {
        (0..n).map(|_| u()).collect()
    }

    pub fn uv2(n: usize) -> Vec<(usize, usize)> {
        (0..n).map(|_| uv(2)).map(|a| (a[0], a[1])).collect()
    }

    pub fn uv3(n: usize) -> Vec<(usize, usize, usize)> {
        (0..n).map(|_| uv(3)).map(|a| (a[0], a[1], a[2])).collect()
    }

    pub fn fv(n: usize) -> Vec<f64> {
        (0..n).map(|_| f()).collect()
    }

    pub fn cmap(h: usize) -> Vec<Vec<char>> {
        (0..h).map(|_| s()).collect()
    }
}