class Token:
    def __init__(self, name, value=None):
        self.name = name
        self.value = value

    def is_a(self, name):
        return self.name == name

    def __str__(self):
        if self.value is not None:
            return f'{self.name}[{self.value}]'
        return f'{self.name}'


class Lexer:
    def __init__(self):
        self.text = ''
        self.cursor = 0

    def scan(self, text):
        self.text = text
        self.cursor = 0

    def next(self):
        self.scan_spaces()

        scanners = [
            self.scan_text('AND', '&'),
            self.scan_text('OR', '|'),
            self.scan_text('IMP', '->'),
            self.scan_text('NOT', '~'),
            self.scan_text('OPAR', '('),
            self.scan_text('CPAR', ')'),
            self.scan_text('COMMA', ','),
            self.scan_keyword('exists'),
            self.scan_keyword('forall'),
            self.scan_var,
            self.scan_const,
            self.scan_pred,
        ]

        for scanner in scanners:
            tok = scanner()
            if tok is not None:
                return tok

        return None

    def peek(self, lookahead=0):
        tok = None
        cursor = self.cursor

        for i in range(lookahead + 1):
            tok = self.next()

        self.cursor = cursor

        return tok

    def scan_spaces(self):
        while self.cursor < len(self.text) \
              and self.text[self.cursor].isspace():
            self.cursor += 1

    def scan_var(self):
        cursor = self.cursor
        value = ''

        while cursor < len(self.text) and (
                self.text[cursor].islower()
                or self.text[cursor].isdigit()
        ):
            value += self.text[cursor]
            cursor += 1

        if value != '':
            self.cursor = cursor
            return Token('VAR', value)

        return None

    def scan_const(self):
        cursor = self.cursor
        value = ''

        while cursor < len(self.text) and (
                self.text[cursor].isupper()
                or self.text[cursor].isdigit()
        ):
            value += self.text[cursor]
            cursor += 1

        if value != '' and self.is_sep(cursor):
            self.cursor = cursor
            return Token('CONST', value)

        return None

    def scan_pred(self):
        cursor = self.cursor
        value = ''

        while cursor < len(self.text) and not self.is_sep(cursor):
            value += self.text[cursor]
            cursor += 1

        format = len(value) > 1 and value[0].isupper() \
            and value[1:].islower()

        if len(value) > 0 and format:
            self.cursor = cursor
            return Token('PRED', value)

        return None

    def scan_keyword(self, name):
        def scanner():
            cursor = self.cursor
            value = ''

            if cursor >= len(self.text) or self.text[cursor] != '\\':
                return None

            cursor += 1
            i = 0

            while cursor < len(self.text) and i < len(name) \
                    and self.text[cursor] == name[i]:
                cursor += 1
                value += name[i]
                i += 1

            if not self.is_sep(cursor):
                return None

            if value == name:
                self.cursor = cursor
                return Token(f'{name.upper()}')

            return None
        return scanner

    def scan_text(self, name, text, tok_value=None):
        def scanner():
            cursor = self.cursor
            value = ''

            i = 0

            while cursor < len(self.text) and i < len(text) \
                    and self.text[cursor] == text[i]:
                cursor += 1
                value += text[i]
                i += 1

            if value == text:
                self.cursor = cursor
                return Token(name, tok_value)

            return None
        return scanner

    def is_sep(self, idx):
        if idx < 0 or idx >= len(self.text):
            return True

        return self.text[idx] in [
            ' ',
            '\n',
            '\t',
            '-',
            '\\',
            '&',
            '|',
            '~',
            '(',
            ')',
            ','
        ]