LIS with Stack

AtCoder

IDabc262_g

Time2000ms

Memory256MB

Difficulty—

There is an empty sequence $X$ and an empty stack $S$. Also, you are given an integer sequence $A=(a_1,\ldots,a_N)$ of length $N$. For each $i=1,\ldots,N$ in this order, Takahashi will do one of the following operations: * Move the integer $a_i$ onto the top of $S$. * Discard the integer $a_i$ from $A$. Additionally, Takahashi may do the following operation whenever $S$ is not empty: * Move the integer at the top of $S$ to the tail of $X$. The score of the final $X$ is defined as follows. * If $X$ is non-decreasing, i.e. if $x_i \leq x_{i+1}$ holds for all integer $i(1 \leq i \lt |X|)$, where $X=(x_1,\ldots,x_{|X|})$, then the score is $|X|$ (where $|X|$ denotes the number of terms in $X$). * If $X$ is not non-decreasing, then the score is $0$. Find the maximum possible score. ## Constraints * $1 \leq N \leq 50$ * $1 \leq a_i \leq 50$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $\ldots$ $a_N$ [samples]

Samples

Input #1

7
1 2 3 4 1 2 3

Output #1

5

The following operations make the final $X$ equal $(1,1,2,3,4)$, for a score of $5$.

*   Move $a_1=1$ onto the top of $S$.
*   Move $1$ at the top of $S$ to the tail of $X$.
*   Move $a_2=2$ onto the top of $S$.
*   Discard $a_3=3$.
*   Move $a_4=4$ onto the top of $S$.
*   Move $a_5=1$ onto the top of $S$.
*   Move $1$ at the top of $S$ to the tail of $X$.
*   Move $a_6=2$ onto the top of $S$.
*   Move $2$ at the top of $S$ to the tail of $X$.
*   Move $a_7=3$ onto the top of $S$.
*   Move $3$ at the top of $S$ to the tail of $X$.
*   Move $4$ at the top of $S$ to the tail of $X$.

We cannot make the score $6$ or greater, so the maximum possible score is $5$.

Input #2

10
1 1 1 1 1 1 1 1 1 1

Output #2

API Response (JSON)

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  "problem": {
    "name": "LIS with Stack",
    "description": {
      "content": "There is an empty sequence $X$ and an empty stack $S$. Also, you are given an integer sequence $A=(a_1,\\ldots,a_N)$ of length $N$.   For each $i=1,\\ldots,N$ in this order, Takahashi will do one of the",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc262_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is an empty sequence $X$ and an empty stack $S$. Also, you are given an integer sequence $A=(a_1,\\ldots,a_N)$ of length $N$.  \nFor each $i=1,\\ldots,N$ in this order, Takahashi will do one of the...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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