# Box Progression Part 1

**Logic**Level 3

\[ \large \square + \square\square+\square\square\square+\square\square\square\square \]

You are given that the numbers \(0,1,2,\ldots,9\) are to be filled in the square boxes as shown above (without repetition) such that it represent a sum of a 1-digit, 2-digit, 3-digit, and 4-digit number.

Of all the possible arrangements, find the **minimum** value of the sum of these four numbers.

**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 \( 1 \times \square \).