Problem Brief

Minimum Insertions to Balance a Parentheses String

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Given a string that consists of left and right parentheses, '(' and ')', balance the parentheses by inserting parentheses as necessary. Determine the minimum number of characters that must be inserted.

Function Description

Complete the function minInsertionsToBalance in the editor.

minInsertionsToBalance has the following parameter:

String s: the initial parentheses sequence

Returns

int: the minimum number of insertions

1Example 1

Input

s = "()))"

Output

Explanation

N/A

2Example 2

Input

s = "(()))"

Output

Explanation

Insert 1 left parenthesis at the left end of the string to get '((()))'. The string is balanced after 1 insertion. s = '))((' Insert 2 left parentheses at the start and 2 right parentheses at the end of the string to get "(())(())" after 4 insertions.

Constraints

Limits and guarantees your solution can rely on.

1 ≤ length of s ≤ 10⁵