Chaos Construction: Increasing Path

Rules:

Place the numbers from 1 to 9 exactly once in every row, column, and region. Each region is orthogonally connected and must be located by the solver. Each region has an index from 1 to 9, and the leftmost cell in a regions topmost row contains the index.

A path that travels orthogonally from cell center to cell center must be found such that it visits each region in the order of their indices from lowest to highest. The path may not re-enter any region, and within any region, numbers strictly increase along the path.

A number in a cell with an arrow or arrows indicates the total count of cells in the same region as itself that are on the path in the indicated directions combined. The cell itself is not counted. If a cell has multiple arrows, at least one cell is on the path in the direction of each arrow.