Score : $200$ points

问题陈述

有一个由 $64$ 个方格组成的棋盘，分为 $8$ 行和 $8$ 列。用 $(i,j)$ 表示从顶部数第 $i$ 行 $(1\leq i\leq8)$ 和从左边数第 $j$ 列 $(1\leq j\leq8)$ 的方格。

每个方格要么为空，要么上面放置了一个棋子。方格的状态由一个长度为 $8$ 的字符串序列 $(S_1,S_2,S_3,\ldots,S_8)$ 表示。如果 $S_i$ 中的第 $j$ 个字符是 .，则方格 $(i,j)$ $(1\leq i\leq8,1\leq j\leq8)$ 为空；如果是 #，则表示有棋子。

你想要在一个 空方格 上放置你的棋子，使得它 不能被任何现有的棋子捕获。

放置在方格 $(i,j)$ 上的棋子可以捕获满足以下任一条件的棋子：

• 放置在第 $i$ 行的方格上
• 放置在第 $j$ 列的方格上

例如，放置在方格 $(4,4)$ 上的棋子可以捕获下图中蓝色显示的方格上的棋子：

你可以在多少个方格上放置你的棋子？

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

There is a grid of $64$ squares with $8$ rows and $8$ columns. Let $(i,j)$ denote the square at the $i$-th row from the top $(1\leq i\leq8)$ and $j$-th column from the left $(1\leq j\leq8)$.

Each square is either empty or has a piece placed on it. The state of the squares is represented by a sequence $(S_1,S_2,S_3,\ldots,S_8)$ of $8$ strings of length $8$. Square $(i,j)$ $(1\leq i\leq8,1\leq j\leq8)$ is empty if the $j$-th character of $S_i$ is ., and has a piece if it is #.

You want to place your piece on an empty square in such a way that it cannot be captured by any of the existing pieces.

A piece placed on square $(i,j)$ can capture pieces that satisfy either of the following conditions:

• Placed on a square in row $i$
• Placed on a square in column $j$

For example, a piece placed on square $(4,4)$ can capture pieces placed on the squares shown in blue in the following figure:

How many squares can you place your piece on?

Constraints

• Each $S_i$ is a string of length $8$ consisting of . and # $(1\leq i\leq 8)$.

Input

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

$S_1$

$S_2$

$S_3$

$S_4$

$S_5$

$S_6$

$S_7$

$S_8$

Output

Print the number of empty squares where you can place your piece without it being captured by any existing pieces.

Sample Input 1

...#....
#.......
.......#
....#...
.#......
........
........
..#.....

Sample Output 1

4

The existing pieces can capture pieces placed on the squares shown in blue in the following figure:

Therefore, you can place your piece without it being captured on $4$ squares: square $(6,6)$, square $(6,7)$, square $(7,6)$, and square $(7,7)$.

Sample Input 2

........
........
........
........
........
........
........
........

Sample Output 2

64

There may be no pieces on the grid.

Sample Input 3

.#......
..#..#..
....#...
........
..#....#
........
...#....
....#...

Sample Output 3

4