Nesting

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:
N is an integer within the range [0..1,000,000];
string S consists only of the characters "(" and/or ")".
Complexity:
expected worst-case time complexity is O(N);
expected worst-case space complexity is O(1) (not counting the storage required for input arguments).
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