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)

#[test]
fn test_solve() {
    assert_eq!(solve("3 3 2\n1 4 3\n2 5 7\n8 9 6\n1\n4 8\n"), "5\n");
    assert_eq!(solve("4 2 3\n3 7\n1 4\n5 2\n6 8\n2\n2 2\n2 2\n"), "0\n0\n");
    assert_eq!(solve("5 5 4\n13 25 7 15 17\n16 22 20 2 9\n14 11 12 1 19\n10 6 23 8 18\n3 21 5 24 4\n3\n13 13\n2 10\n13 13\n"), "0\n5\n0\n");
}
fn solve(src: &str) -> String {
    let mut sc = Scanner::from_str(src);

    let h: usize = sc.read();
    let w: usize = sc.read();
    let d: usize = sc.read();
    let mut ida = vec![(0, 0); h * w];
    for i in 0..h {
        for j in 0..w {
            let a: usize = sc.read();
            ida[a - 1] = (i, j);
        }
    }
    
    let def = |a, b| {
        if a > b {
            a - b
        } else {
            b - a
        }
    };
    let cst = |a, b| {
        let (i, j) = ida[a];
        let (p, q) = ida[b];
        def(i, p) + def(j, q)
    };

    let mut sum = vec![vec![0; h * w / d + 2]; d];
    for r in 0..d {
        let mut i = 0;
        let mut v = i * d + r;
        while v + d < h * w {
            sum[r][i + 1] = sum[r][i] + cst(v, v+d);
            i += 1;
            v += d;
        }
    }

    let mut ret = String::new();
    use std::fmt::Write;

    let q: usize = sc.read();
    for _ in 0..q {
        let l: usize = sc.read();
        let r: usize = sc.read();
        let (l, r) = (l-1, r-1);
        let rem = l % d;
        writeln!(&mut ret, "{}", sum[rem][r/d] - sum[rem][l/d]).unwrap();
    }

    ret
}
fn main() {
    let mut buf = String::new();
    use std::io::{Read, Write};
    std::io::stdin().read_to_string(&mut buf).unwrap();
    std::io::stdout().write_all(solve(&buf).as_bytes()).unwrap();
}
struct Scanner<'a>(std::str::SplitWhitespace<'a>);
impl<'a> Scanner<'a> {
    fn from_str(src: &str) -> Scanner {
        Scanner(src.split_whitespace())
    }
    fn get(&mut self) -> &str {
        self.0.next().unwrap()
    }
    fn read<T: std::str::FromStr>(&mut self) -> T {
        self.get().parse().ok().unwrap()
    }
}