Swap Digit

AtCoder

IDarc154_a

Time2000ms

Memory256MB

Difficulty—

You are given $N$\-digit positive integers $A$ and $B$ whose topmost digits are not $0$. You can repeat the following operation any number of times (possibly zero). * Choose an integer $i$ such that $1 \le i \le N$ and swap the $i$\-th lowest digits of $A$ and $B$. Find the smallest possible value of $A \times B$ after your operations, modulo $998244353$. Note that you are not asked to minimize the remainder when $A \times B$ is divided by $998244353$. ## Constraints * $1 \le N \le 200000$ * $A$ and $B$ are $N$\-digit positive integers whose topmost digits are not $0$. ## Input The input is given from Standard Input in the following format: $N$ $A$ $B$ [samples]

Samples

Input #1

2
13
22

Output #1

276

You can make $A \times B = 276$ by performing the operation once, as follows.

*   Choose $i=1$ to swap the bottommost digits of $A$ and $B$, making $A=12, B=23$.

You cannot make $A \times B = 275$ or less, so the answer is $276$.

Input #2

8
20220122
21002300

Output #2

54558365

Find the value modulo $998244353$.

API Response (JSON)

{
  "problem": {
    "name": "Swap Digit",
    "description": {
      "content": "You are given $N$\\-digit positive integers $A$ and $B$ whose topmost digits are not $0$. You can repeat the following operation any number of times (possibly zero). *   Choose an integer $i$ such tha",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc154_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given $N$\\-digit positive integers $A$ and $B$ whose topmost digits are not $0$.\nYou can repeat the following operation any number of times (possibly zero).\n\n*   Choose an integer $i$ such tha...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments