Tri Outside Sudoku (Daily Sudoku League #45)

This is the Sudoku in which the rules of two Sudoku are merged. One is Tri Sudoku where shaded cells contain three different numbers, another Sudoku is Outside Sudoku.
This is not the new type but I have seen this type appearing in one of the WPF Grand Prix 2013 Sudoku championships last year.

This Tri Outside Sudoku is my 45th contribution to The League of Extraordinary Ladies and Gentlemen. Can you solve this Tri Outside Sudoku puzzle?

Rules of Tri Outside Sudoku

Classic Sudoku Rules apply. Additionally, the grey cells contain only three different digits. Outside clues correspond to digits that are in the first three cells in the corresponding direction.