Insertion

AtCoder

IDabc064_d

Time2000ms

Memory256MB

Difficulty—

You are given a string $S$ of length $N$ consisting of `(` and `)`. Your task is to insert some number of `(` and `)` into $S$ to obtain a _correct bracket sequence_. Here, a correct bracket sequence is defined as follows: * `()` is a correct bracket sequence. * If $X$ is a correct bracket sequence, the concatenation of `(`, $X$ and `)` in this order is also a correct bracket sequence. * If $X$ and $Y$ are correct bracket sequences, the concatenation of $X$ and $Y$ in this order is also a correct bracket sequence. * Every correct bracket sequence can be derived from the rules above. Find the shortest correct bracket sequence that can be obtained. If there is more than one such sequence, find the lexicographically smallest one. ## Constraints * The length of $S$ is $N$. * $1 ≤ N ≤ 100$ * $S$ consists of `(` and `)`. ## Input Input is given from Standard Input in the following format: $N$ $S$ [samples]

Samples

Input #1

3
())

Output #1

(())

Input #2

6
)))())

Output #2

(((()))())

Input #3

8
))))((((

Output #3

(((())))(((())))

API Response (JSON)

{
  "problem": {
    "name": "Insertion",
    "description": {
      "content": "You are given a string $S$ of length $N$ consisting of `(` and `)`. Your task is to insert some number of `(` and `)` into $S$ to obtain a _correct bracket sequence_.   Here, a correct bracket sequenc",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc064_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a string $S$ of length $N$ consisting of `(` and `)`. Your task is to insert some number of `(` and `)` into $S$ to obtain a _correct bracket sequence_.  \nHere, a correct bracket sequenc...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments