Balanced parenthesizations of n pairs HARD Backtracking (BAC) 50 XP 0 solved
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Problem

Read a positive natural number `n`. Generate and print in lexicographic order all expressions formed from exactly `n` opening parentheses `(` and `n` closing parentheses `)` such that the expression is **well-formed** (at every prefix the number of `(` is at least the number of `)`). Lexicographic order treats `(` as smaller than `)`.

Input format

Input input.txt

The program reads from standard input a single natural number, `n`. - `1 <= n <= 6`

Output format

Output output.txt

The program prints all well-formed expressions, one per line, with no spaces between parentheses.

Example

input
3
output
((()))

(()())

(())()

()(())

()()()

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