Almost, just almost

Probability Level 4

We say that a number is almost increasing if for each digit of that number, either that digit is 0 or all digits to the left of it are (strictly) smaller than it. How many 4 digit numbers are almost increasing?

Details and assumptions

As an explicit example, the number $2035$ is almost increasing.

The number $12=012$ is a 2 digit number, not a 3 digit number.