Problem: 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.

Examples

Input

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


Output

1


Input

4 4
1 4
4 1
.##.


.##.


Output

-1


Input

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


Output

0


Input

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


Output

2

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.util.ArrayDeque;
import java.io.InputStreamReader;
import java.io.InputStream;

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

    static class DWizardInMaze {
        static int[] di = {0, 0, 1, -1};
        static int[] dj = {1, -1, 0, 0};
        static int INF = 100000000;
        static int H;
        static int W;

        public void solve(int testNumber, MyScanner sc, PrintWriter out) {
            H = sc.nextInt();
            W = sc.nextInt();
            int fromFirst = sc.nextInt() - 1;
            int fromSecond = sc.nextInt() - 1;
            int toFirst = sc.nextInt() - 1;
            int toSecond = sc.nextInt() - 1;
            char[][] table = sc.nextTable(H);
            ArrayDeque<int[]> queue = new ArrayDeque<>();
            int[][] dist = new int[H][W];
            for (int i = 0; i < H; i++) {
                Arrays.fill(dist[i], INF);
            }
            queue.add(new int[]{fromFirst, fromSecond});
            dist[fromFirst][fromSecond] = 0;
            while (!queue.isEmpty()) {
                int[] tmp = queue.pollFirst();
                int i = tmp[0];
                int j = tmp[1];
                int curDist = dist[i][j];
                for (int k = 0; k < 4; k++) {
                    int ni = i + di[k];
                    int nj = j + dj[k];
                    if (in(ni, nj) && table[ni][nj] == '.' && dist[ni][nj] > curDist) {
                        dist[ni][nj] = curDist;
                        queue.addFirst(new int[]{ni, nj});
                    }
                }
                for (int a = -2; a <= 2; a++) {
                    for (int b = -2; b <= 2; b++) {
                        int ni = i + a;
                        int nj = j + b;
                        if (in(ni, nj) && table[ni][nj] == '.' && dist[ni][nj] > curDist + 1) {
                            dist[ni][nj] = curDist + 1;
                            queue.addLast(new int[]{ni, nj});
                        }
                    }
                }
            }
            int ret = dist[toFirst][toSecond];
            if (ret >= INF) {
                ret = -1;
            }
            out.println(ret);
        }

        static boolean in(int a, int b) {
            return 0 <= a && a < H && 0 <= b && b < W;
        }

    }

    static class MyScanner {
        private BufferedReader br;
        private StringTokenizer tokenizer;

        public MyScanner(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }

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

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public char[][] nextTable(int rows) {
            char[][] ret = new char[rows][];
            for (int i = 0; i < rows; i++) {
                ret[i] = next().toCharArray();
            }
            return ret;
        }

    }
}