The Magnitude Is Important!
\[ \large \square + \square \square + \square \square \square + \square \square \square \square \]
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 \( 1 \times \square \).