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: Runtime Error)



private fun getInts(): IntArray {
    return readLine()!!.split(" ").map {it.toInt()}.toIntArray()
}

private lateinit var originalMap : Array<Array<Char>>
private lateinit var islandIdMap : Array<Array<Int>>
private lateinit var setOfAdjList : Array<MutableSet<Int>>
private var height :Int  = 0
private var width : Int = 0

private fun isSafe(h:Int,w:Int):Boolean {
    return h >=0 && w >= 0 && h < height && w < width
}


fun main(){
    val hw = getInts()
    height = hw[0]
    width = hw[1]
    val start = getInts()
    val goal = getInts()

    // オリジナルを格納
    originalMap = Array(height){arrayOf<Char>()}
    for (i in 0 until height) {
        originalMap[i] = readLine()!!.toCharArray().toTypedArray()
    }

    // 島マップを作る。
    // 島マップの初期化。島index-1を未訪問とする。
    islandIdMap = Array(height){Array(width){-1}}

    // 探索の開始
    var islandCounter = 0
    fun invest(h:Int,w:Int):Boolean {
        if (!isSafe(h,w)){
            // 範囲外
            return false
        }
        if (islandIdMap[h][w] >= 0){
            // 訪問済
            return false
        }
        if (originalMap[h][w] == '#'){
            // 道ではない
            return false
        }
        islandIdMap[h][w] = islandCounter
        invest(h,w+1)
        invest(h,w-1)
        invest(h+1,w)
        invest(h-1,w)
        // 探索が終了したので、この島をカウントする。
        return true
    }
    for (h in 0 until height) {
        for (w in 0 until width) {
            val isNewIsland = invest(h,w)
            if (isNewIsland) {
                islandCounter++
            }
        }
    }
    // islandCounterには島の数が入る。


    // 島の接続関係を調べる。
    // 島隣接setを初期化
    setOfAdjList = Array(islandCounter) {
        mutableSetOf<Int>()
    }
    for (h in 0 until height) {
        for (w in 0 until width) {
            // ワープ可能場所
            val coords = arrayOf(
                Pair(h+2,w+2),
                Pair(h+2,w+1),
                Pair(h+2,w),
                Pair(h+2,w-1),
                Pair(h+2,w-2),

                Pair(h+1,w+2),
                Pair(h+1,w+1),
                Pair(h+1,w),
                Pair(h+1,w-1),
                Pair(h+1,w-2),

                Pair(h,w+2),
                Pair(h,w+1),
                Pair(h,w-1),
                Pair(h,w-2),

                Pair(h-1,w+2),
                Pair(h-1,w+1),
                Pair(h-1,w),
                Pair(h-1,w-1),
                Pair(h-1,w-2),

                Pair(h-2,w+2),
                Pair(h-2,w+1),
                Pair(h-2,w),
                Pair(h-2,w-1),
                Pair(h-2,w-2)
            )
            coords.map {
                if (isSafe(it.first,it.second) &&
                    originalMap[it.first][it.second] != '#' &&
                    originalMap[h][w] != '#'
                ) {
                    val islandOfThis = islandIdMap[h][w]
                    val another = islandIdMap[it.first][it.second]
                    if (islandOfThis != another) {
                        setOfAdjList[islandOfThis].add(another)
                    }
                }
            }
        }
    }

    // 島の幅優先探索
    // 島のワープ回数
    val warpCounter = Array(islandCounter){-1}
    val startIsland = islandIdMap[start[0]-1][start[1]-1]
    val goalIsland = islandIdMap[goal[0]-1][goal[1]-1]
    fun investIsland(count: Int,isLandId:Int) {
        if (warpCounter[isLandId]>=0){
            return
        }
        warpCounter[isLandId] = count
        setOfAdjList[isLandId].map {
            investIsland(count+1,it)
        }
    }
    investIsland(0,startIsland)

//    islandIdMap.map{
//        it.map {
//            print(it)
//            print("\t")
//        }
//        print("\n")
//    }

    print(warpCounter[goalIsland])
}