class ParseError(Exception):
    pass


class Num:
    def __init__(self, value):
        self.value = value

    def __repr__(self):
        return f"Num({self.value!r})"

    def __eq__(self, other):
        return isinstance(other, Num) and self.value == other.value


class BinOp:
    def __init__(self, op: str, left, right):
        self.op = op
        self.left = left
        self.right = right

    def __repr__(self):
        return f"BinOp({self.op!r}, {self.left!r}, {self.right!r})"

    def __eq__(self, other):
        return (isinstance(other, BinOp) and self.op == other.op
                and self.left == other.left and self.right == other.right)


class Unary:
    def __init__(self, op: str, operand):
        self.op = op
        self.operand = operand

    def __repr__(self):
        return f"Unary({self.op!r}, {self.operand!r})"

    def __eq__(self, other):
        return (isinstance(other, Unary) and self.op == other.op
                and self.operand == other.operand)


class _Parser:
    def __init__(self, tokens):
        self._tokens = tokens
        self._pos = 0

    def _current(self):
        return self._tokens[self._pos]

    def _advance(self):
        tok = self._tokens[self._pos]
        if tok.kind != 'EOF':
            self._pos += 1
        return tok

    def _expect(self, kind):
        tok = self._current()
        if tok.kind != kind:
            raise ParseError(f"expected {kind}, got {tok!r}")
        return self._advance()

    def expr(self):
        left = self._term()
        while self._current().kind in ('PLUS', 'MINUS'):
            op = self._advance().value
            right = self._term()
            left = BinOp(op, left, right)
        return left

    def _term(self):
        left = self._unary()
        while self._current().kind in ('STAR', 'SLASH'):
            op = self._advance().value
            right = self._unary()
            left = BinOp(op, left, right)
        return left

    def _unary(self):
        if self._current().kind == 'MINUS':
            self._advance()
            operand = self._unary()
            return Unary('-', operand)
        return self._primary()

    def _primary(self):
        tok = self._current()
        if tok.kind == 'NUMBER':
            self._advance()
            return Num(tok.value)
        if tok.kind == 'LPAREN':
            self._advance()
            node = self.expr()
            self._expect('RPAREN')
            return node
        raise ParseError(f"unexpected token {tok!r}")


def parse(tokens) -> object:
    """Parse a token list (from lexer.tokenize) into an AST.

    Returns the root Node, one of:
      Num(value)               — numeric literal
      BinOp(op, left, right)  — binary +  -  *  /
      Unary(op, operand)       — unary -

    Raises ParseError on malformed input.
    """
    if not tokens or (len(tokens) == 1 and tokens[0].kind == 'EOF'):
        raise ParseError("empty input")
    p = _Parser(tokens)
    node = p.expr()
    if p._current().kind != 'EOF':
        raise ParseError(f"unexpected token after expression: {p._current()!r}")
    return node