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)

#![allow(unused_imports)]
use std::cmp::*;
use std::collections::*;
use itertools::Itertools;
use num::clamp;
use proconio::{input, marker::*, fastout};
use superslice::*;

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

    let mut i2pos = vec![(0, 0); h*w + 1];
    for y in 0..h {
        for x in 0..w {
            let i = a[y][x];
            i2pos[i] = (x as i64, y as i64);
        }
    }

    let mut cost = vec![vec![0; h*w + 1]; 20];
    for i in 1..=h*w - d{ 
        let (x1, y1) = i2pos[i];
        let (x2, y2) = i2pos[i+d];
        cost[0][i] = (x1 - x2).abs() + (y1 - y2).abs();
    }

    for exp in 1..cost.len() {
        let factor = min(h*w, (1<<exp) * d);
        for i in 1..=h*w - factor {
            cost[exp][i] = cost[exp-1][i] + cost[exp-1][i+factor/2];
        }
    }

    for (mut l, r) in lr {
        let mut count = (r - l) / d;
        let mut ans = 0;
        let mut exp = 0;
        while count > 0 {
            while count % 2 == 0 {
                exp += 1;
                count /= 2;
            }
            ans += cost[exp][l];
            l += (1<<exp) * d;
            count -= 1;
        }
        println!("{}", ans);
    }
}