Given a string of parentheses, you must turn it into a well formed string by inserting as few parentheses as possible, at any position (you cannot delete or change any of the existing parentheses).
A well formed string of parentheses is defined by the following rules:
-The empty string is well formed.
-If s is a well formed string, (s) is a well formed string.
-If s and t are well formed strings, their concatenation st is a well formed string.
As examples, "(()())", "" and "(())()" are well formed strings and "())(", "()(" and ")" are malformed strings.
Input a string par of parentheses,and the par will contain between 1 and 60 characters, inclusive.Each character of par will be an opening or closing parenthesis, i.e., '(' or ')'.Proccess to the end of file.
Output the minimum number of parentheses that need to be inserted to make it into a well formed string.