========================================
-- input :  123
-- lexer :
Token(kind='NUMBER',value='123',children=[])
-- parser : 
['EXPRESSION', '', [['TERM', '', [['FACTOR', '', [['NUMBER', '123', []]]]]]]]
-- output :  123
========================================
-- input :  a*b
-- lexer :
Token(kind='IDENTIFIER',value='a',children=[])
Token(kind='MULOP',value='*',children=[])
Token(kind='IDENTIFIER',value='b',children=[])
-- parser : 
[   'EXPRESSION',
    '',
    [   [   'TERM',
            '',
            [   ['FACTOR', '', [['IDENTIFIER', 'a', []]]],
                ['MULOP', '*', []],
                ['TERM', '', [['FACTOR', '', [['IDENTIFIER', 'b', []]]]]]]]]]
-- output :  (* a b)
========================================
-- input :  a + 2 * b
-- lexer :
Token(kind='IDENTIFIER',value='a',children=[])
Token(kind='ADDOP',value='+',children=[])
Token(kind='NUMBER',value='2',children=[])
Token(kind='MULOP',value='*',children=[])
Token(kind='IDENTIFIER',value='b',children=[])
-- parser : 
[   'EXPRESSION',
    '',
    [   ['TERM', '', [['FACTOR', '', [['IDENTIFIER', 'a', []]]]]],
        ['ADDOP', '+', []],
        [   'EXPRESSION',
            '',
            [   [   'TERM',
                    '',
                    [   ['FACTOR', '', [['NUMBER', '2', []]]],
                        ['MULOP', '*', []],
                        [   'TERM',
                            '',
                            [['FACTOR', '', [['IDENTIFIER', 'b', []]]]]]]]]]]]
-- output :  (+ a (* 2 b))
========================================
-- input :  1*c*2*d
-- lexer :
Token(kind='NUMBER',value='1',children=[])
Token(kind='MULOP',value='*',children=[])
Token(kind='IDENTIFIER',value='c',children=[])
Token(kind='MULOP',value='*',children=[])
Token(kind='NUMBER',value='2',children=[])
Token(kind='MULOP',value='*',children=[])
Token(kind='IDENTIFIER',value='d',children=[])
-- parser : 
[   'EXPRESSION',
    '',
    [   [   'TERM',
            '',
            [   ['FACTOR', '', [['NUMBER', '1', []]]],
                ['MULOP', '*', []],
                [   'TERM',
                    '',
                    [   ['FACTOR', '', [['IDENTIFIER', 'c', []]]],
                        ['MULOP', '*', []],
                        [   'TERM',
                            '',
                            [   ['FACTOR', '', [['NUMBER', '2', []]]],
                                ['MULOP', '*', []],
                                [   'TERM',
                                    '',
                                    [   [   'FACTOR',
                                            '',
                                            [['IDENTIFIER', 'd', []]]]]]]]]]]]]]
-- output :  (* 1 (* c (* 2 d)))
========================================
-- input :  a*b+c*d
-- lexer :
Token(kind='IDENTIFIER',value='a',children=[])
Token(kind='MULOP',value='*',children=[])
Token(kind='IDENTIFIER',value='b',children=[])
Token(kind='ADDOP',value='+',children=[])
Token(kind='IDENTIFIER',value='c',children=[])
Token(kind='MULOP',value='*',children=[])
Token(kind='IDENTIFIER',value='d',children=[])
-- parser : 
[   'EXPRESSION',
    '',
    [   [   'TERM',
            '',
            [   ['FACTOR', '', [['IDENTIFIER', 'a', []]]],
                ['MULOP', '*', []],
                ['TERM', '', [['FACTOR', '', [['IDENTIFIER', 'b', []]]]]]]],
        ['ADDOP', '+', []],
        [   'EXPRESSION',
            '',
            [   [   'TERM',
                    '',
                    [   ['FACTOR', '', [['IDENTIFIER', 'c', []]]],
                        ['MULOP', '*', []],
                        [   'TERM',
                            '',
                            [['FACTOR', '', [['IDENTIFIER', 'd', []]]]]]]]]]]]
-- output :  (+ (* a b) (* c d))
========================================
-- input :  123 + abc + z * ( 3 + x )
-- lexer :
Token(kind='NUMBER',value='123',children=[])
Token(kind='ADDOP',value='+',children=[])
Token(kind='IDENTIFIER',value='abc',children=[])
Token(kind='ADDOP',value='+',children=[])
Token(kind='IDENTIFIER',value='z',children=[])
Token(kind='MULOP',value='*',children=[])
Token(kind='LEFTPAREN',value='(',children=[])
Token(kind='NUMBER',value='3',children=[])
Token(kind='ADDOP',value='+',children=[])
Token(kind='IDENTIFIER',value='x',children=[])
Token(kind='RIGHTPAREN',value=')',children=[])
-- parser : 
[   'EXPRESSION',
    '',
    [   ['TERM', '', [['FACTOR', '', [['NUMBER', '123', []]]]]],
        ['ADDOP', '+', []],
        [   'EXPRESSION',
            '',
            [   ['TERM', '', [['FACTOR', '', [['IDENTIFIER', 'abc', []]]]]],
                ['ADDOP', '+', []],
                [   'EXPRESSION',
                    '',
                    [   [   'TERM',
                            '',
                            [   ['FACTOR', '', [['IDENTIFIER', 'z', []]]],
                                ['MULOP', '*', []],
                                [   'TERM',
                                    '',
                                    [   [   'FACTOR',
                                            '',
                                            [   ['LEFTPAREN', '(', []],
                                                [   'EXPRESSION',
                                                    '',
                                                    [   [   'TERM',
                                                            '',
                                                            [   [   'FACTOR',
                                                                    '',
                                                                    [   [   'NUMBER',
                                                                            '3',
                                                                            [   ]]]]]],
                                                        ['ADDOP', '+', []],
                                                        [   'EXPRESSION',
                                                            '',
                                                            [   [   'TERM',
                                                                    '',
                                                                    [   [   'FACTOR',
                                                                            '',
                                                                            [   [   'IDENTIFIER',
                                                                                    'x',
                                                                                    [   ]]]]]]]]]],
                                                [   'RIGHTPAREN',
                                                    ')',
                                                    []]]]]]]]]]]]]]
-- output :  (+ 123 (+ abc (* z (+ 3 x))))