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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Optional;
import java.util.PriorityQueue;
import java.util.StringTokenizer;
import java.util.function.BiConsumer;
import java.util.function.BiFunction;

public class Main {
    private static final int[] walkX = {1, 0, -1, 0};
    private static final int[] walkY = {0, 1, 0, -1};
    private static final int[] warp = {-2, -1, 0, 1, 2};

    /*
    徒歩がコスト0，ワープがコスト1のダイクストラ
     */
    public static void main(final String[] args) {
        final FastScanner scanner = new FastScanner(System.in);
        final int h = scanner.nextInt();
        final int w = scanner.nextInt();

        final BiFunction<Integer, Integer, Boolean> isInside = (x, y) -> x >= 0 && x < h && y >= 0 && y < w;

        final int sx = scanner.nextInt() - 1;
        final int sy = scanner.nextInt() - 1;
        final int dx = scanner.nextInt() - 1;
        final int dy = scanner.nextInt() - 1;

        final int[][] table = new int[h][w];
        for (final int[] array : table) {
            Arrays.fill(array, Integer.MAX_VALUE);
        }
        table[sx][sy] = 0;
        final boolean[][] field = new boolean[h][w];
        for (int i = 0; i < h; i++) {
            final String s = scanner.next();
            for (int j = 0; j < w; j++) {
                field[i][j] = s.charAt(j) == '.';
            }
        }

        final PriorityQueue<Point> queue = new PriorityQueue<>(Comparator.comparingInt(p -> table[p.x][p.y]));
        queue.add(new Point(sx, sy));
        while (!queue.isEmpty()) {
            final Point poll = Optional.ofNullable(queue.poll()).orElseThrow();
            final TriConsumer<Integer, Integer, Integer> move = (nextX, nextY, addition) -> {
                if (!isInside.apply(nextX, nextY)) {
                    return;
                }

                if (!field[nextX][nextY]) {
                    return;
                }

                if (table[nextX][nextY] > table[poll.x][poll.y] + addition) {
                    table[nextX][nextY] = table[poll.x][poll.y] + addition;
                    queue.add(new Point(nextX, nextY));
                }
            };

            for (int i = 0; i < 4; i++) {
                final int nextX = poll.x + walkX[i];
                final int nextY = poll.y + walkY[i];
                move.accept(nextX, nextY, 0);
            }

            for (final int warpX : warp) {
                final int nextX = poll.x + warpX;
                for (final int warpY : warp) {
                    final int nextY = poll.y + warpY;
                    move.accept(nextX, nextY, 1);
                }
            }
        }

        System.out.println(table[dx][dy] < Integer.MAX_VALUE ? table[dx][dy] : -1);
    }

    @FunctionalInterface
    interface TriConsumer<T1, T2, T3> {
        void accept(final T1 t1, final T2 t2, final T3 t3);
    }

    private static class Point {
        final int x;
        final int y;

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

    private static class FastScanner {
        private final BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(final InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

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

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