#include <iostream>
#include <list>
#include <string>
using namespace std;

const int ZERO = 0, LPAREN = 1, RPAREN = 2, COMMA = 3, EOI = 4;

class Scanner
{
public:
	Scanner() {};
	void scan(string & input)
	{
		if(0 == input.size())
		{
			cerr << "Empty input!\n";
			exit(1);
		}
		for(unsigned int i = 0; i < input.size(); ++i)
		{
			switch(input[i])
			{
			case '(':
				_tokens.push_back(LPAREN);
				break;
			case ')':
				_tokens.push_back(RPAREN);
				break;
			case '0':
				_tokens.push_back(ZERO);
				break;
			case ',':
				_tokens.push_back(COMMA);
				break;
			case ' ': case '\t':
				break;
			default:
				cerr << "Bad character (" << static_cast<int>(input[i]) << ")\n";
				exit(1);
			};
		}
		_tokens.push_back(EOI);
	};
	void next_token()
	{
		_tokens.pop_front();
	}
	int token()
	{
		return * (_tokens.begin());
	}
	void printout()
	{
		for(list<int>::iterator it = _tokens.begin(); it != _tokens.end(); ++it)
		{
			cout << ' ';
			if(*it == 0) cout << "ZERO";
			else if(*it == 1) cout << "LPAREN";
			else if(*it == 2) cout << "RPAREN";
			else if(*it == 3) cout << "COMMA";
			else if(*it == 4) cout << "EOF";
			else cout << "CRAP";
		}
		cout << '\n';
	}
private:
	list<int> _tokens;
};
Scanner scanner;

int A(int);
int B(int);
int C(int);

int main()
{
	unsigned int max_depth;
	string buffer;

	cout << "Enter input: ";
	getline(cin, buffer);
	scanner.scan(buffer);

	max_depth = A(0);

	if(EOI != scanner.token())
	{
		cerr << "Expected no more input\n";
		cerr << scanner.token();
	}
	else
	{
		cout << "Your input is valid! Max depth: " << max_depth << '\n';
	}
	return 0;
}

int A(int md)
{
	if(LPAREN == scanner.token())
	{
		scanner.next_token();
		md = B(md + 1);
		if(RPAREN == scanner.token())
		{
			scanner.next_token();
			return md;
		}
		else
		{
			cerr << "Error: A expects ')'\n";
			exit(1);
		}
	}
	else if(ZERO == scanner.token())
	{
		scanner.next_token();
		return md;
	}
	else
	{
		cerr << "Error: A expects '(' or '0'\n";
		exit(1);
	}
}

int B(int md)
{
	int da, dc;
	da = A(md);
	dc = C(md);
	if(da > dc)
	{
		return da;
	}
	else
	{
		return dc;
	}
}

int C(int md)
{
	if(COMMA == scanner.token())
	{
		int da, dc;
		scanner.next_token();
		da = A(md);
		dc = C(md);
		if(da > dc)
		{
			return da;
		}
		else
		{
			return dc;
		}
	}
	return md;
}