John proposes that the number $0123456789$ has the following rules:

1) If it is multiplied by a positive integer n, then the product uses the digits 0 to 9 only once.

2) If
**
n is a multiple of 3
**
, then Rule 1
**
does not apply
**
. Otherwise, Rule 1 applies.

3)The product has at least 10 digits. Any product that has less than 10 digits will have 0s added to the front until it reaches 10 digits.

Because he's a jerk, you want to prove him wrong. So, you search for a counterexample to his proposal. You are finding the smallest possible integer that disproves his proposal.

Does such a integer exist? If it does, what is it? If it doesn't, answer 0.

The answer is 19.

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