Count numbers with non repeating digits less than n

 Idea:

We can break the problem to two sub-problems:

  1. Count special ints with digits smaller than n.
  2. Count special ints with digits the same than n.

Sub-problem 1 is straightforward, we can just use basic combination.
Sub-problem 2 is harder, we can further divide it to two subsub-problems.

  1. Count special ints with digits the same than n. Use 345 as an example.
    1. Count special ints like 1xx and 2xx, where 45 is not a limitation here.
    2. Count special ints like 3xx, which is the same as special ints smaller than 45 and without digit 3.

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