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(10**9);h,w=map(int,input().split());b=[[0]*(w+1)]
for i in range(h):
  b.append([0])
  for j in input():
    if j==".":b[-1].append(1)
    else:b[-1].append(2)
  b[-1].append(0)
b.append([0]*(w+1));d=[[0,1],[0,-1],[1,0],[-1,0]];a=0
def s(i,j):
  global B;B[b[i][j]-1]+=1;v=b[i][j];b[i][j]=0
  for k in d:
    if v^3!=b[i+k[0]][j+k[1]]:continue
    s(i+k[0],j+k[1])
for i in range(1,h+1):
  for j in range(1,w+1):B=[0,0];s(i,j);a+=B[0]*B[1]
print(a)