Problem Statement

There is a grid of cells with $N$ rows and $2N$ columns.
Each cell is painted white or black; overall, exactly $N^2$ cells are painted white and the remaining $N^2$ cells are painted black.

The color of the cell in the $i$-th row from the top ($1 \leq i \leq N$) and the $j$-th column from the left ($1 \leq j \leq 2N$) is represented by the character $S_{i,j}$. If $S_{i,j}$ is ., the cell is white; if it is #, the cell is black.

You may perform the following operation any number of times, $0$ or more.

• Choose $2$ cells that are adjacent by sharing an edge and have different colors, and swap their colors.

Your goal is to make all cells in the left half of the grid ($1 \leq j \leq N$) white and all cells in the right half ($N+1 \leq j \leq 2N$) black.
Find the minimum number of operations required to achieve the goal.

Input

The input is given from standard input in the following format.

$N$
$S_1$
$S_2$
$\vdots$
$S_N$

Partial Score

This problem has partial scoring based on subtasks.

Output

Print the minimum number of operations required to achieve the goal on $1$ line.

Sample

1
#.

1

2
..##
..##

0

3
.#.###
#.#...
##..#.

17