Sequence Decomposing

AtCoder

IDabc134_e

Time2000ms

Memory256MB

Difficulty—

You are given a sequence with $N$ integers: $A = { A_1, A_2, \cdots, A_N }$. For each of these $N$ integers, we will choose a color and paint the integer with that color. Here the following condition must be satisfied: * If $A_i$ and $A_j$ $(i < j)$ are painted with the same color, $A_i < A_j$. Find the minimum number of colors required to satisfy the condition. ## Constraints * $1 \leq N \leq 10^5$ * $0 \leq A_i \leq 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $:$ $A_N$ [samples]

Samples

Input #1

Output #1

2

We can satisfy the condition with two colors by, for example, painting $2$ and $3$ red and painting $1$, $4$, and $5$ blue.

Input #2

Output #2

4

We have to paint all the integers with distinct colors.

API Response (JSON)

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  "problem": {
    "name": "Sequence Decomposing",
    "description": {
      "content": "You are given a sequence with $N$ integers: $A = { A_1, A_2, \\cdots, A_N }$. For each of these $N$ integers, we will choose a color and paint the integer with that color. Here the following condition ",
      "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_e"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a sequence with $N$ integers: $A = { A_1, A_2, \\cdots, A_N }$. For each of these $N$ integers, we will choose a color and paint the integer with that color. Here the following condition ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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