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.util.Arrays;
import java.util.LinkedList;
import java.util.Scanner;

public class Main {
    static Scanner sc = new Scanner(System.in);
    
    static int H, W, sx, sy, ex, ey;
    static boolean wall[][] = new boolean[1005][1005];
    static boolean vis[][] = new boolean[1005][1005];

    static LinkedList<Integer> queueX = new LinkedList<>(),
                            queueY = new LinkedList<>(),
                            cost = new LinkedList<>();
    static int queueSize = 0;

    public static boolean crawl(int x, int y, Integer warpUsed) {
        if (vis[x][y]) return false;
        if (wall[x][y]) return false;
        vis[x][y] = true;

        if (x == ex && y == ey) return true;

        // -- try walking first
        if (crawl(x+1, y, warpUsed)) return true;
        if (crawl(x-1, y, warpUsed)) return true;
        if (crawl(x, y+1, warpUsed)) return true;
        if (crawl(x, y-1, warpUsed)) return true;

        // -- performing Warp spell
        for (int dx = -2; dx <= 2; dx++)
            for (int dy = -2; dy <= 2; dy++)
                if (!wall[x+dx][y+dy] && !vis[x+dx][y+dy]) {
                    queueX.add(x+dx);
                    queueY.add(y+dy);
                    cost.add(warpUsed + 1);
                    queueSize++;
                }
        return false;
    }

    public static void solve() {
        queueX.add(sx); queueY.add(sy);
        cost.add(0);
        queueSize = 1;
        // --
        while (queueSize > 0) {
            Integer x = queueX.pop(), y = queueY.pop(), c = cost.pop();
            queueSize--;
            //System.out.println("Crawling.. x = " + x + " y = " + y + " c = " + c);
            //
            if (crawl(x, y, c)) {
                System.out.println(c);
                return;
            }
        }
        System.out.println(-1);
    }

    public static void main(String[] args) {
        H = sc.nextInt(); W = sc.nextInt();
        sx = sc.nextInt(); sy = sc.nextInt();
        ex = sc.nextInt(); ey = sc.nextInt();
        sx += 1; sy += 1;
        ex += 1; ey += 1;

        for (int i = 0; i < 1005; i++)
            Arrays.fill(wall[i], true);

        // start at (2, 2)
        for (int i = 0; i < H; i++) {
            String s = sc.next();
            for (int j = 0; j < W; j++) {
                wall[i+2][j+2] = (s.charAt(j) == '.' ? false : true);
            }
        }
        solve();
    }
}