Mex Mat

AtCoder

IDarc107_e

Time2000ms

Memory256MB

Difficulty—

Consider an $N \times N$ matrix. Let us denote by $a_{i, j}$ the entry in the $i$\-th row and $j$\-th column. For $a_{i, j}$ where $i=1$ or $j=1$ holds, its value is one of $0$, $1$ and $2$ and given in the input. The remaining entries are defined as follows: * $a_{i,j} = \mathrm{mex}(a_{i-1,j}, a_{i,j-1}) (2 \leq i, j \leq N)$ where $\mathrm{mex}(x, y)$ is defined by the following table: $\mathrm{mex}(x, y)$ $y=0$ $y=1$ $y=2$ $x=0$ $1$ $2$ $1$ $x=1$ $2$ $0$ $0$ $x=2$ $1$ $0$ $0$ How many entries of the matrix are $0, 1,$ and $2$, respectively? ## Constraints * $1 \leq N \leq 500{,}000$ * $a_{i,j}$'s given in input are one of $0$, $1$ and $2$. ## Input Input is given from Standard Input in the following format: $N$ $a_{1, 1}$ $a_{1, 1}$ $...$ $a_{1, N}$ $a_{2, 1}$ $:$ $a_{N, 1}$ [samples]

Samples

Input #1

Output #1

7 4 5

The matrix is as follows:

1 2 0 2
0 1 2 0
0 2 0 1
0 1 2 0

API Response (JSON)

{
  "problem": {
    "name": "Mex Mat",
    "description": {
      "content": "Consider an $N \\times N$ matrix. Let us denote by $a_{i, j}$ the entry in the $i$\\-th row and $j$\\-th column. For $a_{i, j}$ where $i=1$ or $j=1$ holds, its value is one of $0$, $1$ and $2$ and given ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc107_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Consider an $N \\times N$ matrix. Let us denote by $a_{i, j}$ the entry in the $i$\\-th row and $j$\\-th column. For $a_{i, j}$ where $i=1$ or $j=1$ holds, its value is one of $0$, $1$ and $2$ and given ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments