token = res.pop()

			except IndexError as e:

				raise ParsingError(f'The asterisk operator is missing an argument. Pattern: "{pattern}", position {i}')

			res.append(Asterisk(token))

			i += 1

		elif c == ")":

			raise ParsingError(f'An opening parenthesis not found. Pattern: "{pattern}", position: {i}')

		elif c == "|" or c == "+":

			is_alternative = True

			res.append(AlternativeSeparator())

			i += 1

		elif c == "_":

			res.append(Lambda())

			i += 1

		else:

			res.append(Symbol(i+offset, c))

			i += 1

	if is_alternative:

		return Alternative(res)

	else:

		return Chain(res)

class Regexp:

	def __init__(self, pattern):

		r = parse(pattern)

		rules = dict()

		alphabet = set()

		for i in r.list_first():

			c = pattern[i]

			alphabet.add(c)

			key = (-1, c)

			if key not in rules:

				rules[key] = set()

			rules[key].add(i)

		for (i, j) in r.list_neighbours():

			c = pattern[j]

			alphabet.add(c)

			key = (i, c)

			if key not in rules:

				rules[key] = set()

			rules[key].add(j)

		end_states = set(r.list_last())

		if r.is_skippable:

	def normalize(self):

		n = len(self.alphabet_index)

		index = {0: 0}

		queue = deque([0])

		rules = []

		while queue:

			si = queue.popleft()

			row = self.rules[si*n:(si+1)*n]

			for sj in row:

				if sj not in index:

					index[sj] = len(index)

					queue.append(sj)

			rules.extend(index[sj] for sj in row)

		end_states = {index[si] for si in self.end_states if si in index}

		return RegexpDFA(rules, end_states, self.alphabet_index)

	def find_distinguishing_string(self, r):

		if self.rules == r.rules and self.end_states == r.end_states:

			return None

		n = len(product.alphabet_index)

		reverse_alphabet_index = {v: k for (k, v) in product.alphabet_index.items()}

		queue = deque([(0, "")])

		visited = {0}

		while queue:

			(state, acc) = queue.popleft()

			if state in product.end_states:

				return acc

			for (i, target) in enumerate(product.rules[state*n:(state+1)*n]):

				if target not in visited:

					queue.append((target, acc+reverse_alphabet_index[i]))

					visited.add(target)

		assert False

	def _find_equivalent_states(self):

		n = len(self.alphabet_index)

		state_list = list(range(len(self.rules) // n))

		equivalents = {(s1, s2) for (i, s1) in enumerate(state_list) for s2 in state_list[i+1:] if (s1 in self.end_states) == (s2 in self.end_states)}

		ctrl = True

		while ctrl:

			ctrl = False

	def _collapse_states(self, equivalents):

		n = len(self.alphabet_index)

		rules = []

		eq_mapping = dict()

		for (s1, s2) in equivalents:

			eq_mapping[s2] = min(s1, eq_mapping.get(s2, math.inf))

		discard_mapping = dict()

		discard_count = 0

		for i in range(0, len(self.rules), n):

			si = i//n

			if si in eq_mapping:

				discard_count += 1

				continue

			discard_mapping[si] = si - discard_count

			rules.extend(map(lambda st: eq_mapping.get(st, st), self.rules[i:i+n]))

		rules = [discard_mapping[st] for st in rules]

		end_states = {discard_mapping[eq_mapping.get(st, st)] for st in self.end_states}

		return (rules, end_states)

	def _build_product_automaton(self, r):

		n = len(self.alphabet_index)

		m = len(r.rules) // n

		k = len(self.rules) // n

		rules = []

		end_states = set()

		for s1 in range(k):

			row1 = self.rules[s1*n:(s1+1)*n]

			for s2 in range(m):

				row2 = r.rules[s2*n:(s2+1)*n]

				rules.extend([x*m + y for (x, y) in zip(row1, row2)])

				if (s1 in self.end_states) != (s2 in r.end_states):

					end_states.add(s1*m + s2)

		return RegexpDFA(rules, end_states, self.alphabet_index).reduce().normalize()

def test():

	tests = ["", "a", "ab", "aabb", "abab", "abcd", "abcbcdbcd"]

	for pattern in ["a(b|c)", "a*b*", "(ab)*", "a((bc)*d)*", "(a|b)*a(a|b)(a|b)(a|b)", "abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz"]:

		print("#", pattern)

		try:

				let target_hash = encode_set(&target_set);

				let is_end = target_set.iter().any(|st| self.end_states.contains(st));

				if !index_new.contains_key(&target_hash) {

					let target_new = index_new.len();

					index_new.insert(target_hash.clone(), target_new);

					index_multi.insert(target_hash.clone(), target_set);

					compact_rules.extend(iter::repeat(FAIL).take(n));

					stack.push(target_hash.clone());

				}

				compact_rules[index_new[&state_hash]*n + alphabet_index[&c]] = index_new[&target_hash];

				if is_end {

					end_states.insert(index_new[&target_hash]);

				}

			}

		}

		let fail = index_new.len();

		compact_rules = compact_rules.into_iter().map(|st| if st != FAIL {st} else {fail}).collect();

		compact_rules.extend(iter::repeat(fail).take(n));

		return RegexpDFA{rules: compact_rules, end_states, alphabet_index};

	}

}

pub struct RegexpDFA {

	rules: Vec<usize>,

	end_states: HashSet<usize>,

	alphabet_index: HashMap<char, usize>

}

impl RegexpDFA {

	pub fn eval(&self, s: String) -> bool {

		let n = self.alphabet_index.len();

		if n == 0 {

			return s.len() == 0;

		}

		let fail = self.rules.len() / n;

		let mut state = START_DFA;

		for c in s.chars() {

			if let Some(ci) = self.alphabet_index.get(&c) {

				state = self.rules[state*n + ci];

			} else {

				return false;

			}

			if state == fail {

				return false;

			}

		while !queue.is_empty() {

			let si = queue.pop_front().unwrap();

			let row = &self.rules[si*n..(si+1)*n];

			for &sj in row {

				if sj != fail && index[sj] == fail {

					index[sj] = k;

					k += 1;

					queue.push_back(sj);

				}

			}

			rules.extend(row.iter().map(|&st| index[st]));

		}

		let end_states = self.end_states.iter().map(|st| index[*st]).collect();

		return RegexpDFA{rules, end_states, alphabet_index: self.alphabet_index.clone()};

	}

	pub fn find_distinguishing_string(&self, other: &RegexpDFA) -> Option<String> {

		if self.rules == other.rules && self.end_states == other.end_states {

			return None;

		}

		let n = product.alphabet_index.len();

		let reverse_alphabet_index: HashMap<usize, char> = HashMap::from_iter(product.alphabet_index.iter().map(|(&k, &v)| (v, k)));

		let mut queue = VecDeque::from([(0, "".to_string())]);

		let mut visited = HashSet::new();

		while !queue.is_empty() {

			let (state, acc) = queue.pop_front().unwrap();

			if product.end_states.contains(&state) {

				return Some(acc);

			}

			for (i, target) in product.rules[state*n..(state+1)*n].iter().enumerate() {

				if !visited.contains(target) {

					queue.push_back((*target, acc.clone()+&String::from(reverse_alphabet_index[&i])));

					visited.insert(target);

				}

			}

		}

		panic!();

	}

	fn find_equivalent_states(&self) -> Vec<(usize, usize)> {

		let n = self.alphabet_index.len();

		let state_vec: Vec<usize> = (0..self.rules.len()/n).collect();

		let mut eq_mapping: Vec<usize> = ((0..m)).collect();

		for (s1, s2) in equivalents.into_iter() {

			eq_mapping[s2] = eq_mapping[s2].min(s1);

		}

		let mut discard_mapping: Vec<usize> = ((0..m)).collect();

		let mut discard_count = 0;

		for si in 0..m {

			if eq_mapping[si] != si {

				discard_count += 1;

				continue;

			}

			discard_mapping[si] = si-discard_count;

			rules.extend(self.rules[si*n..(si+1)*n].iter().map(|&st| eq_mapping[st]));

		}

		rules = rules.into_iter().map(|st| discard_mapping[st]).collect();

		let end_states = self.end_states.iter().map(|st| discard_mapping[eq_mapping[*st]]).collect();

		return RegexpDFA{rules, end_states, alphabet_index: self.alphabet_index.clone()};

	}

	fn build_product_automaton(&self, other: &RegexpDFA) -> RegexpDFA {

		let n = self.alphabet_index.len();

		let m = other.rules.len() / n;

		let k = self.rules.len() / n;

		let mut rules = vec![];

		let mut end_states = HashSet::new();

		for s1 in 0..k {

			let row1 = &self.rules[s1*n..(s1+1)*n];

			for s2 in 0..m {

				let row2 = &other.rules[s2*n..(s2+1)*n];

				rules.extend(row1.iter().zip(row2.iter()).map(|(x, y)| x*m + y));

				if (self.end_states.contains(&s1)) ^ (other.end_states.contains(&s2)) {

					end_states.insert(s1*m + s2);

				}

			}

		}

		return RegexpDFA{rules, end_states, alphabet_index: self.alphabet_index.clone()}.reduce().normalize();

	}

}