Select Mul

AtCoder

IDabc221_c

Time2000ms

Memory256MB

Difficulty—

You are given an integer $N$. Consider permuting the digits in $N$ and separate them into two **positive integers**. For example, for the integer $123$, there are six ways to separate it, as follows: * $12$ and $3$, * $21$ and $3$, * $13$ and $2$, * $31$ and $2$, * $23$ and $1$, * $32$ and $1$. Here, the two integers after separation must not contain leading zeros. For example, it is not allowed to separate the integer $101$ into $1$ and $01$. Additionally, since the resulting integers must be positive, it is not allowed to separate $101$ into $11$ and $0$, either. What is the maximum possible product of the two resulting integers, obtained by the optimal separation? ## Constraints * $N$ is an integer between $1$ and $10^9$ (inclusive). * $N$ contains two or more digits that are not $0$. ## Input Input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

63

As described in Problem Statement, there are six ways to separate it:

*   $12$ and $3$,
*   $21$ and $3$,
*   $13$ and $2$,
*   $31$ and $2$,
*   $23$ and $1$,
*   $32$ and $1$.

The products of these pairs, in this order, are $36$, $63$, $26$, $62$, $23$, $32$, with $63$ being the maximum.

Input #2

Output #2

100

There are two ways to separate it:

*   $100$ and $1$,
*   $10$ and $10$.

In either case, the product is $100$.

Input #3

998244353

Output #3

939337176

API Response (JSON)

{
  "problem": {
    "name": "Select Mul",
    "description": {
      "content": "You are given an integer $N$. Consider permuting the digits in $N$ and separate them into two **positive integers**. For example, for the integer $123$, there are six ways to separate it, as follows: ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc221_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer $N$. Consider permuting the digits in $N$ and separate them into two **positive integers**.\nFor example, for the integer $123$, there are six ways to separate it, as follows:\n...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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