Box in Box

AtCoder

IDabc309_f

Time2500ms

Memory256MB

Difficulty—

There are $N$ boxes. The $i$\-th box has a shape of a rectangular cuboid whose height, width, and depth are $h_i,w_i$, and $d_i$, respectively. Determine if there are two boxes such that one's height, width, and depth are strictly greater than those of the other after rotating them if necessary. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $1 \leq h_i,w_i,d_i \leq 10^9$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $h_1$ $w_1$ $d_1$ $\vdots$ $h_N$ $w_N$ $d_N$ [samples]

Samples

Input #1

Output #1

Yes

If you rotate the $2$\-nd box to swap its height and depth, the $3$\-rd box will have greater height, depth, and width.

Input #2

Output #2

No

Input #3

2
1 1 2
1 2 2

Output #3

No

API Response (JSON)

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    "name": "Box in Box",
    "description": {
      "content": "There are $N$ boxes. The $i$\\-th box has a shape of a rectangular cuboid whose height, width, and depth are $h_i,w_i$, and $d_i$, respectively. Determine if there are two boxes such that one's height,",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2500,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc309_f"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ boxes. The $i$\\-th box has a shape of a rectangular cuboid whose height, width, and depth are $h_i,w_i$, and $d_i$, respectively.\nDetermine if there are two boxes such that one's height,...",
      "is_translate": false,
      "language": "English"
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}

Full JSON Raw Segments