Bracket Sequencing

AtCoder

IDabc167_f

Time2000ms

Memory256MB

Difficulty—

A **bracket sequence** is a string that is one of the following: 1. An empty string; 2. The concatenation of `(`, $A$, and `)` in this order, for some bracket sequence $A$ ; 3. The concatenation of $A$ and $B$ in this order, for some non-empty bracket sequences $A$ and $B$ / Given are $N$ strings $S_i$. Can a bracket sequence be formed by concatenating all the $N$ strings in some order? ## Constraints * $1 \leq N \leq 10^6$ * The total length of the strings $S_i$ is at most $10^6$. * $S_i$ is a non-empty string consisting of `(` and `)`. ## Input Input is given from Standard Input in the following format: $N$ $S_1$ $:$ $S_N$ [samples]

Samples

Input #1

2
)
(()

Output #1

Yes

Concatenating `(()` and `)` in this order forms a bracket sequence.

Input #2

2
)(
()

Output #2

No

Input #3

4
((()))
((((((
))))))
()()()

Output #3

Yes

Input #4

3
(((
)
)

Output #4

No

API Response (JSON)

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  "problem": {
    "name": "Bracket Sequencing",
    "description": {
      "content": "A **bracket sequence** is a string that is one of the following: 1.  An empty string; 2.  The concatenation of `(`, $A$, and `)` in this order, for some bracket sequence $A$ ; 3.  The concatenation o",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc167_f"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "A **bracket sequence** is a string that is one of the following:\n\n1.  An empty string;\n2.  The concatenation of `(`, $A$, and `)` in this order, for some bracket sequence $A$ ;\n3.  The concatenation o...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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