Problem:
Score : 300 points

Problem Statement

There is a grid with H rows and W columns, where each square is painted black or white.

You are given H strings S_1, S_2, ..., S_H, each of length W.
If the square at the i-th row from the top and the j-th column from the left is painted black, the j-th character in the string S_i is #; if that square is painted white, the j-th character in the string S_i is ..

Find the number of pairs of a black square c_1 and a white square c_2 that satisfy the following condition:

There is a path from the square c_1 to the square c_2 where we repeatedly move to a vertically or horizontally adjacent square through an alternating sequence of black and white squares: black, white, black, white...

Constraints

1 \leq H, W \leq 400

|S_i| = W (1 \leq i \leq H)

For each i (1 \leq i \leq H), the string S_i consists of characters # and ..

Input

Input is given from Standard Input in the following format:

H W
S_1
S_2
:
S_H

Output

Print the answer.

Sample Input 1

3 3
.#.
..#
#..

Sample Output 1

10

Some of the pairs satisfying the condition are ((1, 2), (3, 3)) and ((3, 1), (3, 2)), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.

Sample Input 2

2 4
....
....

Sample Output 2

0

Sample Input 3

4 3
###
###
...
###

Sample Output 3

6

Solution in Kotlin (1.3.71) (judge verdict: Wrong Answer)

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


data class Pos(val x: Int, val y: Int)

class GridBfs(val G: List<String>) {
    val H = G.size
    val W = G[0].length
    private val dx = intArrayOf(0,1,0,-1)
    private val dy = intArrayOf(1,0,-1,0)

    val grp = Array(H){IntArray(W){INF}}
    val mp = mutableMapOf<Int, Int>()

    fun countGoals(group: Int, SX: Int, SY: Int): Int {
        if (grp[SX][SY] < group) return mp[grp[SX][SY]] ?: 0

        val que = ArrayDeque<Pos>()
        que.addLast(Pos(SX, SY))

        val goal = Array(H){IntArray(W){0}}

        while (que.isNotEmpty()) {
            val (x, y) = que.removeFirst()

            grp[x][y] = min(grp[x][y], group)

            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] == G[x][y]) {
                    continue
                }

                if (G[nx][ny] == '.') {
                    goal[nx][ny] = 1
                }

                if (grp[nx][ny] > grp[x][y]) {
                    que.push(Pos(nx, ny))
                }
            }
        }

        val res = goal.map{ it.sum() }.sum()
        mp[group] = res
        return res
    }
}

fun solve() {
    val (H, W) = rd.readListInt()
    val G = (0 until H).map { rd.readString() }

    val gbfs = GridBfs(G)

    val starts = ArrayList<Pos>()
    for (i in 0 until H) {
        for (j in 0 until W) {
            if (G[i][j] == '#') {
                val up = if (i>0) G[i-1][j] else '#'
                val right = if (j<W-1) G[i][j+1] else '#'
                val bottom = if (i<H-1) G[i+1][j] else '#'
                val left = if (0<j) G[i][j-1] else '#'

                if (up=='.' || right=='.'
                        || bottom=='.' || left=='.') {
                    starts.add(Pos(i,j))
                }
            }
        }
    }

    for (i in 0 until starts.size) {
        gbfs.countGoals(i, starts[i].x, starts[i].y)
    }

    var ans = 0
    for (s in starts) {
        val group = gbfs.grp[s.x][s.y]
        if (group<INF) ans += gbfs.mp[group]!!
    }

    println(ans)
}


//val rd = debug.Reader("etc", "aising2019", "c", "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
const 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 To(val idx: Int, val cost: Long)
typealias ALI = ArrayList<Int>
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 readListIntCols: (Int) -> List<List<Int>> = { N -> (0 until N).map { br.readLine().split(' ').map { it.toInt() } } }
    val readListLongCol: (Int) -> List<Long> = { N -> (0 until N).map { readLong() } }
    val readListLongCols: (Int) -> List<List<Long>> = { N -> (0 until N).map { br.readLine().split(' ').map { it.toLong() } } }
    val close: () -> Unit = { br.close() }
    protected fun finalize() { close() }
}