Distinct Sum

Let the 10 letters $A$ to $J$ represent each of the digits $0$ to $9$ (not necessarily in order.

What is the minimum value of $\overline{A} + \overline{BC} + \overline{DEF} + \overline{GHIJ}$?

$\overline{ABC}$ refers to reading the number in decimal base. $\overline{ABC} = 100A + 10B + C$, and not $A \times B \times C$.

Details and assumptions

The letters represent digits. Any of them can be any of the digits.