Almost Magic II: Two Squares, One Column

A magic square is a 3-by-3 grid of numbers whose 8 lines (the 3 rows, the 3 columns and the 2 diagonals) all have the same sum.

An almost magic square is a 3-by-3 grid of positive integers whose 8 line sums differ from each other by at most 1. So there is a number S such that every line sums to either S or S+1. An exact magic square also counts as almost magic.

The board below has 3 rows and 5 columns. It contains two bold-outlined 3-by-3 squares:

the left square is columns 1 to 3;
the right square is columns 3 to 5.

The two squares share the middle column (column 3, shaded). The shared column's three cells belong to both squares.

A 3-by-5 board. A solid bold outline marks the left 3-by-3 square (columns 1-3), and a dashed bold outline marks the right 3-by-3 square (columns 3-5). They overlap in the shaded middle column.

Write a positive integer in each of the 15 cells so that:

all 15 integers are different, and
the left square and the right square are both almost magic. Each square is judged on its own 8 lines, and each square may have its own S.

Question: What is the smallest possible total of the 15 integers?

Answer format: a single integer.