What is Proper?

A number is called proper if each successive digit in the number is either monotonically increasing, or equal to the preceding digit. If 0 is not allowed in any place value, how many 6 digit numbers are proper?

2-Digit Example:

11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 38, 39, 44, 45, 46, 47, 48, 49, 55, 56, 57, 58, 59, 66, 67, 68, 69, 77, 78, 79, 88, 89, 99

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