"""Recursive-descent parser for calc expressions.

Grammar:
    expr    := term (('+' | '-') term)*
    term    := factor (('*' | '/') factor)*
    factor  := '-' factor | primary
    primary := NUMBER | '(' expr ')'

Node shapes:
    Num(value)              — a numeric literal; value is int or float
    BinOp(op, left, right)  — op is one of '+' '-' '*' '/'
    Unary(op, operand)      — op is '-'
"""


class ParseError(Exception):
    pass


class Num:
    __slots__ = ('value',)

    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:
    __slots__ = ('op', 'left', 'right')

    def __init__(self, op, 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:
    __slots__ = ('op', 'operand')

    def __init__(self, op, 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 _peek(self):
        return self._tokens[self._pos]

    def _consume(self, kind=None):
        tok = self._tokens[self._pos]
        if kind and tok.kind != kind:
            raise ParseError(f'expected {kind}, got {tok.kind!r}')
        self._pos += 1
        return tok

    def parse(self):
        if self._peek().kind == 'EOF':
            raise ParseError('empty input')
        node = self._expr()
        if self._peek().kind != 'EOF':
            raise ParseError(f'unexpected token {self._peek().kind!r}')
        return node

    def _expr(self):
        node = self._term()
        while self._peek().kind in ('PLUS', 'MINUS'):
            op = self._consume().value
            right = self._term()
            node = BinOp(op, node, right)
        return node

    def _term(self):
        node = self._factor()
        while self._peek().kind in ('STAR', 'SLASH'):
            op = self._consume().value
            right = self._factor()
            node = BinOp(op, node, right)
        return node

    def _factor(self):
        if self._peek().kind == 'MINUS':
            self._consume()
            operand = self._factor()
            return Unary('-', operand)
        return self._primary()

    def _primary(self):
        tok = self._peek()
        if tok.kind == 'NUMBER':
            self._consume()
            return Num(tok.value)
        if tok.kind == 'LPAREN':
            self._consume()
            node = self._expr()
            if self._peek().kind != 'RPAREN':
                raise ParseError(f'unclosed parenthesis, got {self._peek().kind!r}')
            self._consume()
            return node
        raise ParseError(f'unexpected token {tok.kind!r}')


def parse(tokens):
    """Parse a token list from tokenize() and return an AST node."""
    return _Parser(tokens).parse()