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# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.IO;
using System.Text;
class abc089_d {
    static int __cnt = 0;
    static string __mark = "###";
    static void Main(string[] args) {
#if LOCAL_ENVIRONMENT
        StreamReader __sr = new StreamReader("stdin.txt");
        string __str = __sr.ReadToEnd();
        __sr.Close();
        int __index = __str.IndexOf(__mark, 0);
        while (__index != -1) {
            __index = __str.IndexOf(__mark, __index + __mark.Length);
            __cnt++;
        }
        if (__cnt > 0) {
            Console.Write("Eenter test data no(1-{0})? ", __cnt);
            Console.Out.Flush();
            if (!int.TryParse(Console.ReadLine(), out __cnt)) __cnt = 1;
            Console.WriteLine("Select/Default test data: {0}", __cnt);
        }
        var stdin = new System.IO.StreamReader("stdin.txt");
        Console.SetIn(stdin);
#endif
        SimpleScanner sc = new SimpleScanner(__cnt);
        int H = sc.NextInt(), W = sc.NextInt(), D = sc.NextInt();
        int[,] A = new int[H, W];
        Tuple<int, int>[] No = new Tuple<int, int>[H * W + 1];
        for (var h = 0; h < H; h++) {
            for (var w = 0; w < W; w++) {
                var a = sc.NextInt();
                A[h, w] = a;
                No[a] = Tuple.Create(h, w);
            }
        }
        long[] C = new long[H * W + 1];
        int Q = sc.NextInt();
        for (var q = 0; q < Q; q++) {
            long ans = 0;
            int L = sc.NextInt(), R = sc.NextInt();
            for (var n = L; C[n] == 0 && n <= H*W - D; n+=D) 
                C[n] = Math.Abs(No[n].Item1 - No[n+D].Item1) + Math.Abs(No[n].Item2 - No[n+D].Item2);
            while (L != R) {
                ans += C[L];
                L += D;
            }
            Console.WriteLine(ans);
        }
    } //Main

    public class SimpleScanner {
        private int cnt;
        private string[] items;
        public SimpleScanner(int cnt = 0) {
            this.cnt = 0;
            var sb = new StringBuilder();
            var s = Console.ReadLine();
            while (s != null) {
                sb.Append(s + " ");
                s = Console.ReadLine();
            }
            this.items = sb.ToString().Split(' ');
#if LOCAL_ENVIRONMENT
            if (cnt > 0) {
                int index = Array.IndexOf(this.items, __mark + cnt.ToString());
                this.cnt = index + 1;
            }
            Console.Error.WriteLine("SimpleScanner.cnt: {0}", this.cnt);
            Console.Error.WriteLine("SimpleScanner.items: {0}" , this.items.ToStringA());
#endif
        }
        public void SetCnt(int n) { this.cnt = n; }
        public int NextInt() {
            return int.Parse(this.items[this.cnt++]);
        }
        public long NextLong() {
            return long.Parse(this.items[this.cnt++]);
        }
        public string NextString() {
            return this.items[this.cnt++];
        }
        public int[] NextIntArray(int n) {
            if (n < 1) throw new IndexOutOfRangeException("引数は1以上であること！");
            var result = new int[n];
            for (var i = 0; i < n; i++) result[i] = this.NextInt();
#if LOCAL_ENVIRONMENT
            Console.Error.WriteLine("{0}", result.ToStringA());
#endif
            return result;
        }
        public long[] NextLongArray(int n) {
            if (n < 1) throw new IndexOutOfRangeException("引数は1以上であること！");
            var result = new long[n];
            for (var i = 0; i < n; i++) result[i] = this.NextLong();
#if LOCAL_ENVIRONMENT
            Console.Error.WriteLine("{0}", result.ToStringA());
#endif
            return result;
        }
        public string[] NextStringArray(int n) {
            if (n < 1) throw new IndexOutOfRangeException("引数は1以上であること！");
            var result = new string[n];
            for (var i = 0; i < n; i++) result[i] = this.NextString();
#if LOCAL_ENVIRONMENT
            Console.Error.WriteLine("{0}", result.ToStringA());
#endif
            return result;
        }
        public int[][] NextInt2Col(int n) {
            const int M = 2;
            if (n < 1) throw new IndexOutOfRangeException("引数は1以上であること！");
            int[][] result = new int[M][] {
                new int[n],
                new int[n],
            };
            for (var i = 0; i < n; i++) {
                result[0][i] = this.NextInt();
                result[1][i] = this.NextInt();
            }
#if LOCAL_ENVIRONMENT
            Console.Error.WriteLine("NextInt2Col: [");
            for (var i = 0; i < M; i++)
                Console.Error.WriteLine("  {0},", result[i].ToStringA());
            Console.Error.WriteLine("]");
#endif
            return result;
        }
    }
}
static class Extensions {
    public static string ToStringA<T>(this T[] array, string separator = ", ", string braces = "[]") {
        string bL = braces.Length > 0 ? braces[0].ToString() : "";
        string bR = braces.Length > 1 ? braces[1].ToString() : "";
        return bL + String.Join(separator, array) + bR;
    }
}