Rossini Sudoku

Rules of Rossini Sudoku

Place a digit from 1 to 9 into each of the empty cells so that each digit appears exactly once in each row, column and 3x3 outlined box. Additionally, the arrows indicate that the nearest three digits in the row (column) are in ascending or descending order (increasing towards the direction the arrow is pointing towards). If there is no arrow outside a row/column, the nearest 3 digits therein cannot be in either ascending or descending order.