Balance Checker

StackString

Given a string containing just the characters '(' and ')', determine if the input string is valid. A string is considered valid if all opening parentheses have a corresponding closing parentheses in the correct order.

Example 1

Input

[
  "()"
]

Output

true

Explanation. The string contains one pair of matching parentheses.

Example 2

Input

[
  "(())"
]

Output

true

Explanation. The string contains two nested pairs of matching parentheses.

Example 3

Input

[
  "(()"
]

Output

false

Explanation. The string contains an unmatched opening parenthese.

Example 4

Input

[
  ")("
]

Output

false

Explanation. The parentheses are in the wrong order.

Example 5

Input

[
  "((()"
]

Output

false

Explanation. There is one unmatched opening parenthese.

Example 6

Input

[
  "()()"
]

Output

true

Explanation. The string contains two non-nested pairs of matching parentheses.

Follow-up: How would you extend this problem to handle other types of brackets such as '{}' and '[]'?

Constraints:

The input string will only contain the characters '(' and ')'.

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