$\large \square + \square \square + \square \square \square + \square \square \square \square$

Place distinct digits from 0 through 9 in the boxes to get the minimum possible sum. Submit your answer as this minimum sum.

**Note**: You are allowed to start the number with 0.

**Details and Assumptions**:

- This is an arithmetic puzzle, where $1 \square$ would represent the 2-digit number 19 if $\square = 9$. It does not represent the algebraic expression $1 \times \square$.

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