Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

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

Sample Output 1

1

For example, by walking to (2,2) and then using the magic to travel to (4,4), just one use of magic is enough.

Note that he cannot walk diagonally.

Sample Input 2

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

Sample Output 2

-1

He cannot move from there.

Sample Input 3

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

Sample Output 3

0

No use of magic is needed.

Sample Input 4

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

Sample Output 4

2

Solution in Kotlin (1.3.71) (judge verdict: Accepted)

import java.io.*
import java.util.*
import java.lang.*
import java.lang.Math.*


class GridBfs(val G: Array<String>, val Wall:Char = '#',
              val Aisle:Char = '.') {
    val H = G.size
    val W = G[0].length
    init { }
    private val dx = intArrayOf(0,1,0,-1)
    private val dy = intArrayOf(1,0,-1,0)

    fun distance(SX: Int, SY: Int, GX: Int, GY: Int): Int {
        val dq = ArrayDeque<IntPair>()
        dq.add(IntPair(SX, SY))
        val dist = Array(H){IntArray(W){INF}}
        dist[SX][SY] = 0
        while (dq.isNotEmpty()) {
            val (x, y) = dq.removeFirst()!!
            if (x == GX && y == GY)  break

            for(i in dx.indices) {
                val nx = x + dx[i]; val ny = y + dy[i]
                if (nx<0 || H<=nx || ny<0 || W<=ny) {
                    continue
                }
                if (G[nx][ny] == Wall) {
                    continue
                }
                if (dist[nx][ny] > dist[x][y]) {
                    dist[nx][ny] = dist[x][y]
                    dq.addFirst(IntPair(nx, ny))
                }
            }

            for (i in x-2 .. x+2) {
                for (j in y-2 .. y+2) {
                    if (i<0 || H<=i || j<0 || W<=j) {
                        continue
                    }
                    if (G[i][j] == Wall) {
                        continue
                    }

                    if (dist[i][j] > dist[x][y]+1) {
                        dist[i][j] = dist[x][y]+1
                        dq.addLast(IntPair(i, j))
                    }
                }
            }
        }
        if (dist[GX][GY] != INF) {
            return dist[GX][GY]
        } else {
            return -1
        }
    }
}

fun solve() {
    val (H,W) = rd.readIntArray()
    val (SX, SY) = rd.readIntArray().map{it-1}
    val (GX, GY) = rd.readIntArray().map{it-1}
    val G = Array(H){""}
    for (i in 0 until H) {
        G[i] = rd.readString()
    }

    val gb = GridBfs(G)

    val ans = gb.distance(SX, SY, GX, GY)

    println(ans)
}


//val rd = debug.Reader("abc", "176", "d", "sample-1")
val rd = Reader()


fun main(args: Array<String>) {
    try {
        var exception: Throwable? = null
        val sth = Thread(null, SolveThread(), "solveThread", 128 * 1024 * 1024)
        sth.setUncaughtExceptionHandler { _, e -> exception = e }
        sth.start(); sth.join()
        if (exception != null) throw exception!! }
    catch (e: Exception) { throw e }
    finally { rd.close() }
}
const val MOD = 1_000_000_007L; const val INF = Int.MAX_VALUE/2; const val LINF = Long.MAX_VALUE/2
val EPS = 1e-9; fun DBLEQ(a: Double, b: Double): Boolean {return abs(a - b) < EPS}
data class IntPair(val first: Int, val second: Int); data class LongPair(val first: Long, val second: Long)
data class To(val idx: Int, val cost: Long)
fun <T>edge(V: Int): Array<ArrayList<T>> { return Array(V){ArrayList<T>()} }
val errPrintln: (Any) -> Unit = { msg -> System.err.println(msg) }
fun rAssert(exp: Boolean, lazyMsg: () -> String = {""}) {
    if (!exp) { val msg = lazyMsg(); errPrintln("EAssert Error: $msg"); throw Error(msg) }
}
fun tAssert(exp: Boolean, lazyMsg: () -> String = {""}) {
    if (!exp) { val msg = lazyMsg(); errPrintln("TAssert Error: $msg"); Thread.sleep(3000) }
}
class SolveThread : Runnable {
    override fun run() { solve() }
}
class Reader {
    private val br = BufferedReader(InputStreamReader(System.`in`))
    val readString: () -> String = { br.readLine() }
    val readInt: () -> Int = { br.readLine().toInt() }
    val readLong: () -> Long = { br.readLine().toLong() }
    val readIntArray: () -> IntArray = { br.readLine().split(' ').map { it.toInt() }.toIntArray() }
    val readLongArray: () -> LongArray = { br.readLine().split(' ').map { it.toLong() }.toLongArray() }
    val readListInt: () -> List<Int> = { br.readLine().split(' ').map { it.toInt() } }
    val readListLong: () -> List<Long> = { br.readLine().split(' ').map { it.toLong() } }
    val readListIntCol: (Int) -> List<Int> = { N -> (0 until N).map { readInt() } }
    val readListLongCol: (Int) -> List<Long> = { N -> (0 until N).map { readLong() } }
    val close: () -> Unit = { br.close() }
    protected fun finalize() { close() }
}