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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <iomanip>
#include <sstream>
#include <vector>
#include <string>
#include <set>
#include <unordered_set>
#include <map>
#include <unordered_map>
#include <stack>
#include <queue>
#include <deque>
#include <algorithm>
#include <functional>
#include <iterator>
#include <limits>
#include <numeric>
#include <utility>
#include <type_traits>
#include <cmath>
#include <cassert>
#include <cstdio>

using namespace std;
using namespace placeholders;

using LL = long long;
using ULL = unsigned long long;
using VI = vector< int >;
using VVI = vector< vector< int > >;
using VS = vector< string >;
using ISS = istringstream;
using OSS = ostringstream;
using PII = pair< int, int >;
using VPII = vector< pair< int, int > >;
template < typename T = int > using VT = vector< T >;
template < typename T = int > using VVT = vector< vector< T > >;
template < typename T = int > using LIM = numeric_limits< T >;

template < typename T > inline istream& operator>>( istream &s, vector< T > &v ){ for ( T &t : v ) { s >> t; } return s; }
template < typename T > inline ostream& operator<<( ostream &s, const vector< T > &v ){ for ( int i = 0; i < int( v.size() ); ++i ){ s << ( " " + !i ) << v[i]; } return s; }

void in_impl(){};
template < typename T, typename... TS > void in_impl( T &head, TS &... tail ){ cin >> head; in_impl( tail ... ); }
#define IN( T, ... ) T __VA_ARGS__; in_impl( __VA_ARGS__ );

template < typename T > struct getv_fmt;
template <> struct getv_fmt<       int >{ static constexpr const char *fmt = "%d"; };
template <> struct getv_fmt< long long >{ static constexpr const char *fmt = "%lld"; };
template < typename T > void getv( std::vector< T > &v ){ for_each( begin( v ), end( v ), []( T &a ){ scanf( getv_fmt< T >::fmt, &a ); } ); };

template < typename T > inline T fromString( const string &s ) { T res; istringstream iss( s ); iss >> res; return res; }
template < typename T > inline string toString( const T &a ) { ostringstream oss; oss << a; return oss.str(); }

#define NUMBERED( name, number ) NUMBERED2( name, number )
#define NUMBERED2( name, number ) name ## _ ## number
#define REP1( n ) REP2( NUMBERED( REP_COUNTER, __LINE__ ), n )
#define REP2( i, n ) REP3( i, 0, n )
#define REP3( i, m, n ) for ( int i = ( int )( m ); i < ( int )( n ); ++i )
#define GET_REP( a, b, c, F, ... ) F
#define REP( ... ) GET_REP( __VA_ARGS__, REP3, REP2, REP1 )( __VA_ARGS__ )
#define FOR( e, c ) for ( auto &&e : c )
#define ALL( c ) begin( c ), end( c )
#define AALL( a ) ( remove_all_extents< decltype( a ) >::type * )a, ( remove_all_extents< decltype( a ) >::type * )a + sizeof( a ) / sizeof( remove_all_extents< decltype( a ) >::type )
#define DRANGE( c, p ) begin( c ), begin( c ) + ( p ), end( c )

#define SZ( v ) ( (int)( v ).size() )
#define EXIST( c, e ) ( ( c ).find( e ) != ( c ).end() )

template < typename T > inline bool chmin( T &a, const T &b ){ if ( b < a ) { a = b; return true; } return false; }
template < typename T > inline bool chmax( T &a, const T &b ){ if ( a < b ) { a = b; return true; } return false; }

#define PB push_back
#define EM emplace
#define EB emplace_back
#define BI back_inserter

#define MP make_pair
#define fst first
#define snd second

#define DUMP( x ) cerr << #x << " = " << ( x ) << endl

class UnionFind
{
private:
	const int N;

	vector<int> parent;
	vector<int> rank;

	int groups_;
	std::vector< int > sizes;

public:
	UnionFind( int n ) : N( n ), parent( N ), rank( N, 0 ), groups_( N ), sizes( N, 1 )
	{
		std::iota( parent.begin(), parent.end(), 0 );

		return;
	}

	int find( int x )
	{
		if ( parent[x] == x )
		{
			return x;
		}
		return parent[x] = find( parent[x] );
	}

	bool same( int x, int y )
	{
		return find( x ) == find( y );
	}

	bool unite( int x, int y )
	{
		x = find( x );
		y = find( y );

		if ( x == y )
		{
			return false;
		}

		if ( rank[x] < rank[y] )
		{
			parent[x] = y;
			sizes[y] += sizes[x];
		}
		else
		{
			parent[y] = x;
			sizes[x] += sizes[y];

			if ( rank[x] == rank[y] )
			{
				++rank[x];
			}
		}

		--groups_;
		return true;
	}

	int groups() const
	{
		return groups_;
	}

	int groupSize( const int x )
	{
		return sizes[ find( x ) ];
	}
};
// UnionFind( N )
// find( x )
// same( x, y )
// unite( x, y )
// groups()
// groupSize( x )

int main()
{
	cin.tie( 0 );
	ios::sync_with_stdio( false );
	cout << setprecision( 12 ) << fixed;

	IN( int, H, W );
	VS board( H );
	cin >> board;

	UnionFind uf( H * W );
	const auto idx = [&]( const int y, const int x )
	{
		return W * y + x;
	};

	REP( i, H )
	{
		REP( j, W )
		{
			if ( i + 1 < H && board[i][j] != board[ i + 1 ][j] )
			{
				uf.unite( idx( i, j ), idx( i + 1, j ) );
			}
			if ( j + 1 < W && board[i][j] != board[i][ j + 1 ] )
			{
				uf.unite( idx( i, j ), idx( i, j + 1 ) );
			}
		}
		
	}

	map< int, int > blacks, whites;
	REP( i, H )
	{
		REP( j, W )
		{
			++( board[i][j] == '.' ? whites : blacks )[ uf.find( idx( i, j ) ) ];
		}
	}

	LL res = 0;
	FOR( p, blacks )
	{
		const int g = p.fst;
		res += LL( blacks[g] ) * whites[g];
	}
	cout << res << endl;

	return 0;
}