Problem: 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.

Examples

Input

3 3
.#.
..#
#..


Output

10


Input

3 3
.#.
..#
..


Output

10


Input

2 4
....
....


Output

0


Input

4 3


...


Output

6

Solution (in PYTHON3):

Solution:
import sys
sys.setrecursionlimit(1000000)

h,w = [int(i) for i in input().split()]
board = [input() for _ in range(h)]

used = [[0]*w for _ in range(h)]
dx=[ 0, 1, 0,-1]
dy=[ 1, 0,-1, 0]

def dfs(x, y):
    global numb, numw #numbたちがグローバル変数だと教えてあげる
    #(x,y)地点を訪問済みにする
    used[x][y] = 1
    #(x,y)地点での処理を行う（マスの色をカウントするなど）
    if board[x][y] == '#':
        numb += 1
    else:
        numw += 1
    #foreach((nx,ny) \in (x,y)のお隣さん){(nx,ny)に訪問していないとき、dfs(nx,ny)} 
    for i in range(4):
        nx = x + dx[i]
        ny = y + dy[i]
        if nx < 0 or nx >= h or ny < 0 or ny >= w or used[nx][ny] == 1: continue #範囲外参照 or (nx,ny)は確認済み スキップ
        if board[x][y]!=board[nx][ny]: #さらに(nx,ny)と(x,y)がつながっている場合(nx,ny)を訪問
            dfs(nx,ny)
    return #情報をもらうとき：返り値、各地点の情報のみで更新：グローバル変数、情報を送るとき：引数

ans=0
for i in range(h):
    for j in range(w):
        numw = 0
        numb = 0
        if used[i][j] == 1: continue #すでに確認した地点は見ない
        dfs(i,j)
        ans += numw*numb

print(ans)