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 Scala (2.11.7) (judge verdict: Accepted)

import scala.io.StdIn
import scala.annotation.tailrec
import scala.collection.mutable.HashMap

object Main extends App {
  val Array(h, w) = StdIn.readLine.split(" ").map(_.toInt)
  val table = Iterator.continually(StdIn.readLine)
    .take(h)
    .map(_.map(_ == '#').toArray)
    .toArray

  @inline
  def flat(i:Int, j:Int):Int = i * w + j

  val ans = {
    val dx = Array(0, 1, 0, -1)
    val dy = Array(-1, 0, 1, 0)
    val uft = new UnionFindTree(flat(h, w))

    for{
      i <- 0 until h
      j <- 0 until w
    } {
        val ij = flat(i,j)
        (0 until 4).foreach(k => {
          val y = i + dy(k)
          val x = j + dx(k)
          if(0 <= y && y < h && 0 <= x && x < w &&
              table(i)(j) != table(y)(x) ) {
            uft.unite(ij, flat(y,x))
          }
        })
    }
    uft.map.values./:(0L)((acc,e) => {
      acc + e._1.toLong * e._2.toLong
    })
  }

  println(ans)

  class UnionFindTree(n:Int) {
    private val par  = Array.range(0, n)
    private val rank = Array.fill(n)(1)
    val map = HashMap.empty[Int,(Int,Int)]

    def root(x:Int):Int = {
      if(par(x) == x) x
      else { par(x) = root(par(x)); par(x) }
    }

    def isSame(x:Int, y:Int):Boolean = root(x) == root(y)

    def unite(x:Int, y:Int):Unit = {
      val rx = root(x)
      val ry = root(y)
      if(rx == ry) return

      if(!map.contains(ry)) map(ry) = if(table(ry/w)(ry%w)) (1,0) else (0,1)
      if(!map.contains(rx)) map(rx) = if(table(rx/w)(rx%w)) (1,0) else (0,1)
      val ryv = map(ry)
      val rxv = map(rx)

      if(rank(rx) < rank(ry)) {
        par(rx) = ry
        map(ry) = (ryv._1 + rxv._1, ryv._2 + rxv._2)
        map -= rx
      }
      else {
        par(ry) = rx
        if(rank(rx) == rank(ry)) rank(rx) += 1
        map(rx) = (rxv._1 + ryv._1, rxv._2 + ryv._2)
        map -= ry
      }
    }
  }
}