3^N Minesweeper

AtCoder

IDabc288_g

Time2000ms

Memory256MB

Difficulty—

There is zero or one bomb at each of positions $0, 1, 2, \ldots, 3^N-1$. Let us say that positions $x$ and $y$ are **neighboring** each other if and only if the following condition is satisfied for every $i=1, \ldots, N$. * Let $x'$ and $y'$ be the $i$\-th lowest digits of $x$ and $y$ in ternary representation, respectively. Then, $|x' - y'| \leq 1$. It is known that there are exactly $A_i$ bombs in total at the positions neighboring position $i$. Print a placement of bombs consistent with this information. ## Constraints * $1 \leq N \leq 12$ * There is a placement of bombs consistent with $A_0, A_1, \ldots, A_{3^N-1}$. * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_0$ $A_1$ $\ldots$ $A_{3^N-1}$ [samples]

Samples

Input #1

1
0 1 1

Output #1

0 0 1

Position $0$ is neighboring positions $0$ and $1$, which have $0$ bombs in total.  
Position $1$ is neighboring positions $0$, $1$, and $2$, which have $1$ bomb in total.  
Position $2$ is neighboring positions $1$ and $2$, which have $1$ bombs in total.  
If there is a bomb at only position $2$, all conditions above are satisfied, so this placement is correct.

Input #2

2
2 3 2 4 5 3 3 4 2

Output #2

0 1 0 1 0 1 1 1 0

Input #3

2
0 0 0 0 0 0 0 0 0

Output #3

0 0 0 0 0 0 0 0 0

API Response (JSON)

{
  "problem": {
    "name": "3^N Minesweeper",
    "description": {
      "content": "There is zero or one bomb at each of positions $0, 1, 2, \\ldots, 3^N-1$.   Let us say that positions $x$ and $y$ are **neighboring** each other if and only if the following condition is satisfied for ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc288_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is zero or one bomb at each of positions $0, 1, 2, \\ldots, 3^N-1$.  \nLet us say that positions $x$ and $y$ are **neighboring** each other if and only if the following condition is satisfied for ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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