Disconnected Counting Chaos

This puzzle is a variant of Chaos Construction that allows regions to be diagonally connected. The rules are similar to a puzzle by KNT.

Rules

Place the digits 1 to 9 exactly once in every row, column, and region. The regions must be determined by the solver. The cells within each region are connected orthogonally and/or diagonally.

A digit in a cell with a red X indicates the size of the orthogonally connected section of the region that cell belongs to. All possible red Xs are given.

A digit in a cell with arrows indicates the number of cells that are in the same region as the cell with arrows in the indicated directions combined, including itself. If a cell does not belong to the same orthogonally connected section of the region as the cell with arrows, it is counted three times.

6x6 Example Puzzle

Puzzle Links