Smallest unseen, but no sharing digits! Challenge

Here at PPCG, we sure do like our sequences, so here's a fun another one.

Let's define a(n) as being the smallest non-negative integer X that is not equal to any a(k) (0 &lt; k &lt; n), and a(n-1) and X do not share any decimal digits. a(0) = 0

Given an input n &gt; 0, output such a(n).

For example, for input n = 13, we have a(13) = 20, since a(12) = 11 and 20 is the smallest non-negative integer we haven't seen yet that doesn't share any decimal digits with 11.

Sequence

Here are the first 20 terms to get you started. This is sequence A067581 on OEIS.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 22, 11, 20, 13, 24, 15, 23, 14, 25


Rules


The input and output can be assumed to fit in your language's native integer type.
The input and output can be given in any convenient format.
You can choose to either 0-index, as I am here in my examples, or 1-index for your submission. Please state which you're doing.
Either a full program or a function are acceptable. If a function, you can return the output rather than printing it.
If possible, please include a link to an online testing environment so other people can try out your code!
Standard loopholes are forbidden.
This is code-golf so all usual golfing rules apply, and the shortest code (in bytes) wins.
Python 2, 85 bytes

-1 byte thanks to Dead Possum 


n=0,
exec"i=0\nwhile set(`i`)&amp;set(`n[-1]`)or i in n:i+=1\nn+=i,;"*input()
print n[-1]


Try it online!