Problem Statement

There is a grid with $H$ rows and $W$ columns. Each cell has one of the characters +, -, # written on it. Let $(i,j)$ denote the cell at the $i$-th row from the top and the $j$-th column from the left. The grid is given by $H$ length-$W$ strings $S_1, S_2 , \dots ,S_H$: the $j$-th character of $S_i$ is written on $(i,j)$.

You can perform the following operation zero or more times:

• Choose one cell that is not #. Change to # all cells that are "reachable from the chosen cell only by moving to an adjacent cell in the left, right, or down direction without passing through a cell that is #." Here, the chosen cell itself is included among the reachable cells.

Find the maximum possible value of the following value in the grid after the operations: the number of + cells minus the number of - cells.

Constraints

• $1 \le H,W \le 30$
• $S_i$ is a string of length $W$ consisting of +, -, #.
• $H$ and $W$ are integers.

Input

The input is given from Standard Input in the following format:

• $H$ $W$
• $S_1$
• $S_2$
• $\vdots$
• $S_H$

Output

Output the answer.

2 3
+-+
--+

1

If you choose $(2,1)$, all cells in row $2$ change to # (note that you cannot move upward). The remaining row $1$ has two cells of + and one cell of -, so the value is $2-1=1$, and this is the maximum.

3 3
+--
-#-
#+#

1

If you choose $(1,1)$, all cells except $(3, 2)$ become #. Note that the chosen cell $(1, 1)$ itself is included among the reachable cells, and that you cannot pass through a cell that is #.

5 7
++#--++
-+---+#
##++-++
--#-++-
+---#++

5

• Source: AtCoder ABC 472 G