Diagonal Separation 2

AtCoder

IDabc442_f

Time2000ms

Memory256MB

Difficulty—

There is a grid with $N$ rows and $N$ columns. The square at the $i$\-th row from the top and $j$\-th column from the left is denoted as square $(i, j)$. Each square in the grid is painted white or black. The information of the grid is given by $N$ strings $S_1, S_2, \ldots, S_N$. If the $j$\-th character of $S_i$ is `.`, square $(i, j)$ is painted white; if the $j$\-th character of $S_i$ is `#`, square $(i, j)$ is painted black. You will repaint some squares so that both of the following conditions are satisfied: * For every row, the following condition holds: * There exists an integer $k$ satisfying $0 \leq k \leq N$ such that the leftmost $k$ squares of that row are painted white and the other squares are painted black. * For every column, the following condition holds: * There exists an integer $k$ satisfying $0 \leq k \leq N$ such that the topmost $k$ squares of that column are painted white and the other squares are painted black. Find the minimum number of squares that need to be repainted to satisfy the conditions. ## Constraints * $1 \leq N \leq 5000$ * $N$ is an integer. * $S_i$ is a string of length $N$ consisting of `.` and `#`. ## Input The input is given from Standard Input in the following format: $N$ $S_1$ $S_2$ $\vdots$ $S_N$ [samples]

Samples

Input #1

3
..#
#.#
.#.

Output #1

2

You can satisfy the conditions by repainting square $(2, 1)$ white and square $(3, 3)$ black.

Input #2

5
..#.#
#..##
###.#
.###.
#....

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Diagonal Separation 2",
    "description": {
      "content": "There is a grid with $N$ rows and $N$ columns. The square at the $i$\\-th row from the top and $j$\\-th column from the left is denoted as square $(i, j)$. Each square in the grid is painted white or bl",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc442_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a grid with $N$ rows and $N$ columns. The square at the $i$\\-th row from the top and $j$\\-th column from the left is denoted as square $(i, j)$.\nEach square in the grid is painted white or bl...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments