Rossini Sudoku

Rossini Sudoku is a logical puzzle. Arrows on the edge of the grid indicate the direction in which the first three numbers are arranged in ascending order.

Rules: In each cell of the 9×9 grid, enter a number in the range 1–9. Each number must appear exactly once in each row, column, and block.
Additional rules: An arrow at the edge of the grid shows the direction in which the first three numbers in the corresponding row or column are sorted in ascending order. If no arrow is present, the first three numbers are sorted neither in ascending nor in descending order.