find all balanced braces
void find_balanced_braces(size_t const &n, size_t open, size_t close, size_t index, string &s, vector<string> &res){
if(open == n and close == n)
res.push_back(s);
else{
if(open < n){
s[index] = '(';
find_balanced_braces(n, open+1, close, index+1, s, res);
}
if(close < open){
s[index] = ')';
find_balanced_braces(n, open, close+1, index+1, s, res);
}
}
}
find_balanced_braces(n, 0, 0, 0, s, res);