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)]
#![allow(unused_variables)]
#![allow(dead_code)]

fn main() {
    let (H, W, D): (usize, usize, usize) = {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        let mut iter = line.split_whitespace();
        (
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap()
        )
    };
    let A: Vec<Vec<usize>> = {
        let mut A = vec![];
        for _ in 0..H {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            A.push(
                line.split_whitespace()
                    .map(|x| x.parse().unwrap())
                    .collect()
            );
        }
        A
    };
    let Q: usize = {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        line.trim().parse().unwrap()
    };
    let (L, R): (Vec<usize>, Vec<usize>) = {
        let (mut L, mut R) = (vec![], vec![]);
        for _ in 0..Q {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            L.push(iter.next().unwrap().parse().unwrap());
            R.push(iter.next().unwrap().parse().unwrap());
        }
        (L, R)
    };

    let N = H * W;
    let mut X = vec![0; N + 1];
    let mut Y = vec![0; N + 1];
    for i in 0..H {
        for j in 0..W {
            let a = A[i][j];
            X[a] = j as i64;
            Y[a] = i as i64;
        }
    }
    let mut dp = vec![0; N + 1];
    for i in (D + 1)..(N + 1) { dp[i] = dp[i - D] + (X[i] - X[i - D]).abs() + (Y[i] - Y[i - D]).abs(); }

    let ans = (0..Q)
        .map(|i| (dp[R[i]] - dp[L[i]]).to_string())
        .collect::<Vec<_>>()
        .join("\n");

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