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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder2 {
	class Program {
		static void Main(string[] args) {

		　　var inputArray = retreiveLongArray();
			var inputCount = 3;

			// 不正な入力は処理しない
			if (inputArray.Length != inputCount) {
				Console.WriteLine("invalid input");
				return;
			}
			var H = (int)inputArray[0];
			var W = (int)inputArray[1];
			var D = (int)inputArray[2];

			var zahhyou = new Dictionary<int, Tuple<int, int>>();

			for (int i = 0; i < H; i++) {
				var inp = retreiveLongArray();
				for (int j = 0; j < W; j++) {
					var input = (int)inp[j];
					zahhyou.Add(input, new Tuple<int, int>(i, j));
				}
			}
			var Q = retreiveLongArray()[0];
			var Questions = new List<Tuple<int, int>>();

			for (int i = 0; i < Q; i++) {
				var inp = retreiveLongArray();
				Questions.Add(new Tuple<int, int>((int)inp[0], (int)inp[1]));
			}
			var ruiseki = new Dictionary<int, int>();
			for (int i = 1; i <= D; i++) {
				ruiseki.Add(i, 0);
				var k = i+D;
				var previous = zahhyou[i];
				while (k <= H*W) {
					var current = zahhyou[k];
					var distanse = Math.Abs(current.Item1 - previous.Item1) + Math.Abs(current.Item2 - previous.Item2);
					ruiseki.Add(k, ruiseki[k - D] + distanse);
					previous = current;
					k += D;
				}

			}
			foreach (var question in Questions) {
				Console.WriteLine(ruiseki[question.Item2] - ruiseki[question.Item1]);
			}



		}

		/// <summary>
		/// スペースで区切られた文字列配列の入力を受け取る
		/// </summary>
		/// <returns></returns>
		private static string[] retreiveStringArray() {
			var inputArray = Console.ReadLine().Split(' ');
			return inputArray;
		}

		/// <summary>
		/// スペースで区切られた整数配列の入力を受け取る
		/// </summary>
		/// <returns></returns>
		private static long[] retreiveLongArray() {
			var inputArray = Console.ReadLine().Split(' ');
			var longArray = inputArray.Select(s => long.Parse(s));
			return longArray.ToArray();
		}
	}
}