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.Closeable;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedHashMap;
import java.util.LinkedList;
import java.util.ListIterator;
import java.util.Map.Entry;

import java.util.PriorityQueue;
import java.util.Random;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;


public class Main {
	
	public static boolean in_range(int x, int y, int W, int H) {
		return 0 <= x && x < W && 0 <= y && y < H;
	}
	
	public static final int[][] move_dirs = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}}; 
	
	public static void main(String[] args) throws IOException {	
		try(final Scanner sc = new Scanner(System.in)){
			final int H = sc.nextInt();
			final int W = sc.nextInt();
			
			final int ch = sc.nextInt() - 1;
			final int cw = sc.nextInt() - 1;
			
			final int dh = sc.nextInt() - 1;
			final int dw = sc.nextInt() - 1;
			
			char[][] board = new char[H][];
			for(int i = 0; i < H; i++) {
				board[i] = sc.next().toCharArray();
			}
			
			int[][] costs = new int[H][W];
			for(int i = 0; i < H; i++) {
				for(int j = 0; j < W; j++) {
					costs[i][j] = Integer.MAX_VALUE;
				}
			}
			
			LinkedList<Integer> queue = new LinkedList<Integer>();
			queue.add(cw); queue.add(ch); queue.add(0);
			costs[ch][cw] = 0;
			
			while(!queue.isEmpty()) {
				final int x = queue.poll();
				final int y = queue.poll();
				final int cost = queue.poll();
				
				if(costs[y][x] < cost) { continue; }
				
				for(final int[] moves : move_dirs) {
					final int nx = x + moves[0];
					final int ny = y + moves[1];
					
					if(!in_range(nx, ny, W, H)) { continue; }
					if(board[ny][nx] != '.') { continue; }
					
					if(costs[ny][nx] <= cost) { continue; }
					costs[ny][nx] = cost;
					queue.addFirst(cost); queue.addFirst(ny); queue.addFirst(nx);
				}
				
				for(int ny = y - 2; ny <= y + 2; ny++) {
					for(int nx = x - 2; nx <= x + 2; nx++) {
						if(!in_range(nx, ny, W, H)) { continue; }
						if(board[ny][nx] != '.') { continue; }
						
						final int next_cost = cost + 1;
						if(costs[ny][nx] <= next_cost) { continue; }
						costs[ny][nx] = next_cost;
						queue.add(nx); queue.add(ny); queue.add(next_cost);
					}
				}
			}
			
			System.out.println(costs[dh][dw] == Integer.MAX_VALUE ? -1 : costs[dh][dw]);
		}
	}

	public static class Scanner implements Closeable {
		private BufferedReader br;
		private StringTokenizer tok;

		public Scanner(InputStream is) throws IOException {
			br = new BufferedReader(new InputStreamReader(is));
		}

		private void getLine() throws IOException {
			while(!hasNext()){
				tok = new StringTokenizer(br.readLine());
			}
		}

		private boolean hasNext() {
			return tok != null && tok.hasMoreTokens();
		}

		public String next() throws IOException {
			getLine();
			return tok.nextToken();
		}

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

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
		

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public int[] nextIntArray(int n) throws IOException {
			final int[] ret = new int[n];
			for(int i = 0; i < n; i++){
				ret[i] = this.nextInt();
			}
			return ret;
		}

		public long[] nextLongArray(int n) throws IOException {
			final long[] ret = new long[n];
			for(int i = 0; i < n; i++){
				ret[i] = this.nextLong();
			}
			return ret;
		}

		public void close() throws IOException {
			br.close();
		}
	}
}