Preparing Boxes

AtCoder

IDabc134_d

Time2000ms

Memory256MB

Difficulty—

There are $N$ empty boxes arranged in a row from left to right. The integer $i$ is written on the $i$\-th box from the left $(1 \leq i \leq N)$. For each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it. We say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied: * For every integer $i$ between $1$ and $N$ (inclusive), the total number of balls contained in the boxes with multiples of $i$ written on them is congruent to $a_i$ modulo $2$. Does there exist a good set of choices? If the answer is yes, find one good set of choices. ## Constraints * All values in input are integers. * $1 \leq N \leq 2 \times 10^5$ * $a_i$ is $0$ or $1$. ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $a_2$ $...$ $a_N$ [samples]

Samples

Input #1

3
1 0 0

Output #1

1
1

Consider putting a ball only in the box with $1$ written on it.

*   There are three boxes with multiples of $1$ written on them: the boxes with $1$, $2$, and $3$. The total number of balls contained in these boxes is $1$.
*   There is only one box with a multiple of $2$ written on it: the box with $2$. The total number of balls contained in these boxes is $0$.
*   There is only one box with a multiple of $3$ written on it: the box with $3$. The total number of balls contained in these boxes is $0$.

Thus, the condition is satisfied, so this set of choices is good.

Input #2

5
0 0 0 0 0

Output #2

0

Putting nothing in the boxes can be a good set of choices.

API Response (JSON)

{
  "problem": {
    "name": "Preparing Boxes",
    "description": {
      "content": "There are $N$ empty boxes arranged in a row from left to right. The integer $i$ is written on the $i$\\-th box from the left $(1 \\leq i \\leq N)$. For each of these boxes, Snuke can choose either to put",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc134_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ empty boxes arranged in a row from left to right. The integer $i$ is written on the $i$\\-th box from the left $(1 \\leq i \\leq N)$.\nFor each of these boxes, Snuke can choose either to put...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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