Crossing

AtCoder

IDtenka1_2018_d

Time2000ms

Memory256MB

Difficulty—

You are given an integer $N$. Determine if there exists a tuple of subsets of ${1,2,...N}$, $(S_1,S_2,...,S_k)$, that satisfies the following conditions: * Each of the integers $1,2,...,N$ is contained in exactly two of the sets $S_1,S_2,...,S_k$. * Any two of the sets $S_1,S_2,...,S_k$ have exactly one element in common. If such a tuple exists, construct one such tuple. ## Constraints * $1 \leq N \leq 10^5$ * $N$ is an integer. ## Input Input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

Yes
3
2 1 2
2 3 1
2 2 3

It can be seen that $(S_1,S_2,S_3)=({1,2},{3,1},{2,3})$ satisfies the conditions.

Input #2

Output #2

No

API Response (JSON)

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  "problem": {
    "name": "Crossing",
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      "content": "You are given an integer $N$. Determine if there exists a tuple of subsets of ${1,2,...N}$, $(S_1,S_2,...,S_k)$, that satisfies the following conditions: *   Each of the integers $1,2,...,N$ is conta",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
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    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "tenka1_2018_d"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer $N$. Determine if there exists a tuple of subsets of ${1,2,...N}$, $(S_1,S_2,...,S_k)$, that satisfies the following conditions:\n\n*   Each of the integers $1,2,...,N$ is conta...",
      "is_translate": false,
      "language": "English"
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}

Full JSON Raw Segments