Classified

AtCoder

IDjsc2019_qual_d

Time2000ms

Memory256MB

Difficulty—

AtCoder's head office consists of $N$ rooms numbered $1$ to $N$. For any two rooms, there is a direct passage connecting these rooms. For security reasons, Takahashi the president asked you to set a **level** for every passage, which is a positive integer and must satisfy the following condition: * For each room $i\ (1 \leq i \leq N)$, if we leave Room $i$, pass through some passages whose levels are all equal and get back to Room $i$, the number of times we pass through a passage is always even. Your task is to set levels to the passages so that the highest level of a passage is minimized. ## Constraints * $N$ is an integer between $2$ and $500$ (inclusive). ## Input Input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

1 2
1

The following image describes this output:
![image](https://img.atcoder.jp/jsc2019-qual/D-sample.png)
For example, if we leave Room $2$, traverse the path $2 \to 3 \to 2 \to 3 \to 2 \to 1 \to 2$ while only passing passages of level $1$ and get back to Room $2$, we pass through a passage six times.

API Response (JSON)

{
  "problem": {
    "name": "Classified",
    "description": {
      "content": "AtCoder's head office consists of $N$ rooms numbered $1$ to $N$. For any two rooms, there is a direct passage connecting these rooms. For security reasons, Takahashi the president asked you to set a *",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "jsc2019_qual_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "AtCoder's head office consists of $N$ rooms numbered $1$ to $N$. For any two rooms, there is a direct passage connecting these rooms.\nFor security reasons, Takahashi the president asked you to set a *...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments