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.IOException;
import java.io.InputStream;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Collections;
import java.util.Comparator;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.NoSuchElementException;
import java.util.Objects;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.TreeMap;
import java.util.TreeSet;

public class Main {

	static Scanner sc = new Scanner(System.in);

	static class FastScanner {
		private final InputStream in;
		private final byte[] buffer = new byte[1024];
		private int ptr = 0;
		private int buflen = 0;

		public FastScanner(InputStream source) {
			in = source;
		}

		private boolean hasNextByte() {
			if (ptr < buflen) {
				return true;
			} else {
				ptr = 0;
				try {
					buflen = in.read(buffer);
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (buflen <= 0) {
					return false;
				}
			}
			return true;
		}

		private int readByte() {
			if (hasNextByte())
				return buffer[ptr++];
			else
				return -1;
		}

		private static boolean isPrintableChar(int c) {
			return 33 <= c && c <= 126;
		}

		public boolean hasNext() {
			while (hasNextByte() && !isPrintableChar(buffer[ptr]))
				ptr++;
			return hasNextByte();
		}

		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (isPrintableChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			long n = 0;
			boolean minus = false;
			int b = readByte();
			if (b == '-') {
				minus = true;
				b = readByte();
			}
			if (b < '0' || '9' < b) {
				throw new NumberFormatException();
			}
			while (true) {
				if ('0' <= b && b <= '9') {
					n *= 10;
					n += b - '0';
				} else if (b == -1 || !isPrintableChar(b)) {
					return minus ? -n : n;
				} else {
					throw new NumberFormatException();
				}
				b = readByte();
			}
		}

		public int nextInt() {
			long nl = nextLong();
			if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
				throw new NumberFormatException();
			return (int) nl;
		}

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

	/**
	 * Compute n! mod. p, (n!)^(-1) mod.p
	 *
	 * @param fac[]
	 *            : n! mod. p
	 * @param finv[]
	 *            : (n!)^(-1) mod. p
	 * @param MAX
	 *            :
	 * @param MOD
	 *            :
	 */

	static void hz_COMinit(long fac[], long finv[], long inv[], final int MAX, final long MOD) {
		fac[0] = fac[1] = 1L;
		finv[0] = finv[1] = 1L;
		inv[1] = 1L;
		for (int i = 2; i < MAX; i++) {
			fac[i] = fac[i - 1] * i % MOD;
			inv[i] = MOD - inv[(int) (MOD % i)] * (MOD / i) % MOD;
			finv[i] = finv[i - 1] * inv[i] % MOD;
		}
	}
	/*
	 * static void hz_COMinit(long fac[], long finv[], long inv[],final int MAX,
	 * final long MOD) { fac[0] = fac[1] = 1L; finv[0] = finv[1] = 1L; inv[1] =
	 * 1L; for (int i = 2; i < MAX; i++){ fac[i] = (BigInteger.valueOf(fac[i -
	 * 1]).multiply(BigInteger.valueOf(i)).mod(BigInteger.valueOf(MOD))).
	 * longValue(); inv[i] =
	 * (BigInteger.valueOf(MOD).subtract(BigInteger.valueOf(inv[(int)(MOD%i)]).
	 * multiply(BigInteger.valueOf(MOD/i)).mod(BigInteger.valueOf(MOD)))).
	 * longValue(); finv[i] = (BigInteger.valueOf(finv[i -
	 * 1]).multiply(BigInteger.valueOf(inv[i])).mod(BigInteger.valueOf(MOD))).
	 * longValue(); } }
	 */

	/**
	 * @Compute nCk(二項係数計算) mod. p
	 * @param fac[]
	 *            : n! mod. p
	 * @param finv[]
	 *            : (n!)^(-1) mod. p
	 * @return :nCk(二項係数計算) mod. p
	 */
	static long hz_COM(long fac[], long finv[], int n, int k, final long MOD) {
		if (n < k)
			return 0;
		if (n < 0 || k < 0)
			return 0;
		return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
	}
	/*
	 * static long hz_COM(long fac[],long finv[], int n, int k, final long MOD){
	 * if (n < k) return 0; if (n < 0 || k < 0) return 0; return
	 * BigInteger.valueOf(fac[n]) .multiply(BigInteger.valueOf(finv[k])
	 * .multiply(BigInteger.valueOf(finv[n - k])) .mod(BigInteger.valueOf(MOD))
	 * ) .mod(BigInteger.valueOf(MOD)).longValue(); }
	 */

	static int hz_swap(int a, int b) {
		if (a >= b)
			return a;
		else
			return b;
	}

	static long hz_swap(long a, long b) {
		if (a >= b)
			return a;
		else
			return b;
	}

	// mod上での差分
	static long hz_modSub(long a, long b, long mod) {
		long v = a - b;
		if (v < 0)
			v += mod;
		return v % mod;
	}

	// mod上での割算
	static long hz_modDiv(long a, long b, long mod) {
		return (a % mod) * hz_modInv(b, mod) % mod;
	}

	// 逆元
	static long hz_modInv(long a, long mod) {
		return hz_modPow(a, mod - 2L, mod);
	}

	// mod上での累乗
	static long hz_modPow(long n, long k, long mod) {

		long result = 1L;

		// k を右シフトしつつ n を 2 乗していく
		while (k > 0L) {
			// k の最下ビットが 1 なら、今の n を答えに掛ける
			if ((k & 1L) == 1L)
				result = (result * n) % mod;
			n = n * n % mod;
			k >>= 1L;
		}

		return result;
	}

	// Union Find Tree
	static class HZ_UF {

		public int[] par;
		public int[] rank;

		public HZ_UF(int n) {
			this.par = new int[n + 1];
			this.rank = new int[n + 1];

			Arrays.fill(par, -1);
			Arrays.fill(rank, 0);
		}

		public void unite(int x, int y) {
			link(root(x), root(y));
		}

		public boolean link(int x, int y) {
			if (x == y)
				return false;
			if (rank[x] > rank[y]) {
				par[x] += par[y];
				par[y] = x;
			} else {
				par[y] += par[x];
				par[x] = y;
				if (rank[x] == rank[y])
					rank[y]++;
			}
			return true;
		}

		public boolean isSame(int x, int y) {
			return root(x) == root(y);
		}

		public int root(int x) {
			if (par[x] < 0)
				return x;
			else
				return x = root(par[x]);
		}

		public int size(int x) {
			return -par[root(x)];
		}
	}

	public static void main(String[] args) {

		solve_abc176_d();
	}
  
  	public static void solve_abc176_d() {

		FastScanner sc = new FastScanner(System.in);
		
		int[][] warp = new int[1001][1001];
		
		int h = sc.nextInt();
		int w = sc.nextInt();
		
		int ch = sc.nextInt();
		int cw = sc.nextInt();
		int dh = sc.nextInt();
		int dw = sc.nextInt();
		
		for(int i=1;i<=h;i++){
			String s = sc.next();
			for(int j=1;j<=w;j++){
				if(s.charAt(j-1) ==  '.'){
					warp[i][j] = Integer.MAX_VALUE;
				}
				else{
					warp[i][j] =-1;
				}
			}
		}
		
		PriorityQueue<solve_abc176_d_pos> pq
			= new PriorityQueue<>((p1,p2)->Integer.compare(p1.num,p2.num));
		
		solve_abc176_d_pos start = new solve_abc176_d_pos(0, ch, cw);
		
		pq.offer(start);
		warp[ch][cw] = 0;
		
		while(!pq.isEmpty()){
			
			solve_abc176_d_pos now = pq.poll(); 
			
			int x0 = now.x;
			int x1 = now.x - 1;
			int x2 = now.x + 1;
			int y0 = now.y;
			int y1 = now.y - 1;
			int y2 = now.y + 1;
			
			int numWarpNow = now.num;
			
			//System.out.println(x0 + "\t" + y0 + "\t" + numWarpNow);
			
			if(x1 >= 1 && warp[x1][y0] > numWarpNow){
				warp[x1][y0] = warp[x0][y0];
				pq.offer(new solve_abc176_d_pos(numWarpNow, x1, y0));
			}
			if(x2 <= h  && warp[x2][y0] > numWarpNow){
				warp[x2][y0] = warp[x0][y0];
				pq.offer(new solve_abc176_d_pos(numWarpNow, x2, y0));
			}
			if(y1 >= 1 && warp[x0][y1] > numWarpNow){
				warp[x0][y1] = warp[x0][y0];
				pq.offer(new solve_abc176_d_pos(numWarpNow, x0, y1));
			}
			if(y2 <= w  && warp[x0][y2] > numWarpNow){
				warp[x0][y2] = warp[x0][y0];
				pq.offer(new solve_abc176_d_pos(numWarpNow, x0, y2));
			}
			
			for(int i=-2;i<=2;i++){
				if(!((x0+i >= 1) && (x0+i <= h))) continue;
				for(int j=-2;j<=2;j++){
					if(!((y0+j >= 1) && (y0+j <= w))) continue;
					
					if(warp[x0+i][y0+j] > numWarpNow + 1){
						warp[x0+i][y0+j] = numWarpNow + 1;
						pq.offer(new solve_abc176_d_pos(numWarpNow+1, x0+i, y0+j));
					}
				}
			}
			
		}
		
		if(warp[dh][dw] == Integer.MAX_VALUE) warp[dh][dw] = -1;
		
		System.out.println(warp[dh][dw]);
		
		//while pq != isEmpty
		
		// pos = pq.poll
		
		//if  warp[x+1][y] > warp
			// warp[x+1][y] = warp
			// pq.offer(pos);
		
		// for i = -2 ,+2
			//for j = -2 to +2
				//if warp[x+i][y+j] > warp
		
	}
	
	public static class solve_abc176_d_pos{
		public int getNum() {
			return num;
		}
		public void setNum(int num) {
			this.num = num;
		}
		public int getX() {
			return x;
		}
		public void setX(int x) {
			this.x = x;
		}
		public int getY() {
			return y;
		}
		public void setY(int y) {
			this.y = y;
		}
		solve_abc176_d_pos(int num, int x, int y){
			this.num = num;
			this.x = x;
			this.y = y;
		};
		int num;
		int x;
		int y;
	}
	
}