Problem:
Score : 400 points

Problem Statement

A maze is composed of a grid of H \times W squares - H vertical, W horizontal.

The square at the i-th row from the top and the j-th column from the left - (i,j) - is a wall if S_{ij} is # and a road if S_{ij} is ..

There is a magician in (C_h,C_w). He can do the following two kinds of moves:

Move A: Walk to a road square that is vertically or horizontally adjacent to the square he is currently in.

Move B: Use magic to warp himself to a road square in the 5\times 5 area centered at the square he is currently in.

In either case, he cannot go out of the maze.

At least how many times does he need to use the magic to reach (D_h, D_w)?

Constraints

1 \leq H,W \leq 10^3

1 \leq C_h,D_h \leq H

1 \leq C_w,D_w \leq W

S_{ij} is # or ..

S_{C_h C_w} and S_{D_h D_w} are ..

(C_h,C_w) \neq (D_h,D_w)

Input

Input is given from Standard Input in the following format:

H W
C_h C_w
D_h D_w
S_{11}\ldots S_{1W}
\vdots
S_{H1}\ldots S_{HW}

Output

Print the minimum number of times the magician needs to use the magic. If he cannot reach (D_h,D_w), print -1 instead.

Sample Input 1

4 4
1 1
4 4
..#.
..#.
.#..
.#..

Sample Output 1

1

For example, by walking to (2,2) and then using the magic to travel to (4,4), just one use of magic is enough.

Note that he cannot walk diagonally.

Sample Input 2

4 4
1 4
4 1
.##.
####
####
.##.

Sample Output 2

-1

He cannot move from there.

Sample Input 3

4 4
2 2
3 3
....
....
....
....

Sample Output 3

0

No use of magic is needed.

Sample Input 4

4 5
1 2
2 5
#.###
####.
#..##
#..##

Sample Output 4

2

Solution in Java (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.ArrayDeque;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        DWizardInMaze solver = new DWizardInMaze();
        solver.solve(1, in, out);
        out.close();
    }

    static class DWizardInMaze {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int h = in.readInt(), w = in.readInt();
            int ch = in.readInt() - 1, cw = in.readInt() - 1;
            int dh = in.readInt() - 1, dw = in.readInt() - 1;


            String[] grid = in.readStringArray(h);


            int[][] seen = new int[h + 1][w + 1];

            ArrayUtils.fill(seen, Integer.MAX_VALUE);

            ArrayDeque<int[]> queue = new ArrayDeque<>();
            queue.add(new int[]{ch, cw});
            seen[ch][cw] = 0;

            int[] dx = {0, 0, -1, 1};
            int[] dy = {1, -1, 0, 0};

            while (!queue.isEmpty()) {
                int[] cur = queue.poll();

                int cost = seen[cur[0]][cur[1]];

                for (int i = 0; i < 4; ++i) {
                    int x = cur[0] + dx[i];
                    int y = cur[1] + dy[i];
                    if (Math.min(x, y) >= 0 && x < h && y < w && grid[x].charAt(y) == '.' && seen[x][y] > cost) {
                        queue.addFirst(new int[]{x, y});
                        seen[x][y] = cost;
                    }
                }

                for (int i = -2; i < 3; ++i)
                    for (int j = -2; j < 3; ++j) {
                        int x = cur[0] + i;
                        int y = cur[1] + j;
                        if (Math.min(x, y) >= 0 && x < h && y < w && grid[x].charAt(y) == '.' && seen[x][y] > cost + 1) {
                            queue.add(new int[]{x, y});
                            seen[x][y] = cost + 1;
                        }
                    }
            }

            out.printLine(seen[dh][dw] == Integer.MAX_VALUE ? -1 : seen[dh][dw]);


        }

    }

    static class ArrayUtils {
        public static void fill(int[][] array, int value) {
            for (int[] row : array) {
                Arrays.fill(row, value);
            }
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void printLine(int i) {
            writer.println(i);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public String[] readStringArray(int size) {
            String[] array = new String[size];
            for (int i = 0; i < size; i++) {
                array[i] = readString();
            }
            return array;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}