On the Subject of Chinese Counting

Do you buy your china in China?

This module contains four keys, each with a Chinese number on them, and two LEDs.

Using the left LED as the row and the right LED as the column, consult the table below to get an order in which to press the keys.

White Red Green Orange
White A C H D
Red H D A C
Green C H D A
Orange H A C D

A = Ascending in value
D = Descending in value
C = Ascending in number of characters, descending in value in ties
H = Descending in number of characters, ascending in value in ties

16
27
38
49
510

N.B.: Multiples of 10 are expressed using a number, and then 十. (For example, 20 is 二十.)