This is a test from a real interview.
A string S consisting of N characters is called properly nested if:
S is empty
S has the form "(U)" where U is a properly nested string
S has the form "VW" where V and W are properly nested strings
For example, string "(()(())())" is properly nested but string "())" isn't. Write a function int solution(char *S); that, given a string S consisting of N characters, returns 1 if string S is properly nested and 0 otherwise. For example, given S = "(()(())())", the function should return 1 and given S = "())", the function should return 0, as explained above. Assume that the string S consists only of the characters "(" and/or ")".