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 11.0.6) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.Arrays;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.BufferedOutputStream;
import java.io.UncheckedIOException;
import java.nio.charset.Charset;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.util.ArrayDeque;
import java.io.InputStream;

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

    static class DWizardInMaze {
        public void solve(int testNumber, LightScanner in, LightWriter out) {
            int h = in.ints(), w = in.ints();
            int sy = in.ints() - 1, sx = in.ints() - 1;
            int gy = in.ints() - 1, gx = in.ints() - 1;
            char[][] s = in.chars(h);
            int[][] d = new int[h][w];
            ArrayUtil.fill(d, h * w);
            d[sy][sx] = 0;
            ArrayDeque<DWizardInMaze.P> q = new ArrayDeque<>();
            q.offer(new DWizardInMaze.P(sx, sy));
            while (!q.isEmpty()) {
                DWizardInMaze.P p = q.poll();
                for (int dx = -2; dx <= 2; dx++) {
                    int nx = p.x + dx;
                    if (nx < 0 || w <= nx) continue;
                    for (int dy = -2; dy <= 2; dy++) {
                        if (dx == 0 && dy == 0) continue;
                        int ny = p.y + dy;
                        if (ny < 0 || h <= ny || s[ny][nx] == '#') continue;
                        int c = Math.abs(dx) + Math.abs(dy) == 1 ? 0 : 1;
                        if (d[ny][nx] <= d[p.y][p.x] + c) continue;
                        d[ny][nx] = d[p.y][p.x] + c;
                        if (c == 0) q.offerFirst(new DWizardInMaze.P(nx, ny));
                        else q.offerLast(new DWizardInMaze.P(nx, ny));
                    }
                }
            }
            if (d[gy][gx] >= h * w) out.ans(-1).ln();
            else out.ans(d[gy][gx]).ln();
        }

        private static class P {
            int x;
            int y;

            P(int x, int y) {
                this.x = x;
                this.y = y;
            }

        }

    }

    static class LightWriter implements AutoCloseable {
        private final Writer out;
        private boolean autoflush = false;
        private boolean breaked = true;

        public LightWriter(Writer out) {
            this.out = out;
        }

        public LightWriter(OutputStream out) {
            this(new OutputStreamWriter(new BufferedOutputStream(out), Charset.defaultCharset()));
        }

        public LightWriter print(char c) {
            try {
                out.write(c);
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter print(String s) {
            try {
                out.write(s, 0, s.length());
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter ans(String s) {
            if (!breaked) {
                print(' ');
            }
            return print(s);
        }

        public LightWriter ans(int i) {
            return ans(Integer.toString(i));
        }

        public LightWriter ln() {
            print(System.lineSeparator());
            breaked = true;
            if (autoflush) {
                try {
                    out.flush();
                } catch (IOException ex) {
                    throw new UncheckedIOException(ex);
                }
            }
            return this;
        }

        public void close() {
            try {
                out.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }

    static class LightScanner implements AutoCloseable {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public LightScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public String string() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new UncheckedIOException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public char[] chars() {
            return string().toCharArray();
        }

        public char[][] chars(int h) {
            char[][] res = new char[h][];
            for (int i = 0; i < h; i++) res[i] = chars();
            return res;
        }

        public int ints() {
            return Integer.parseInt(string());
        }

        public void close() {
            try {
                this.reader.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }

    static final class ArrayUtil {
        private ArrayUtil() {
        }

        public static void fill(int[] a, int v) {
            Arrays.fill(a, v);
        }

        public static void fill(int[][] a, int v) {
            for (int i = 0; i < a.length; i++) {
                fill(a[i], v);
            }
        }

    }
}