Greater than sudoku

This is the penultimate puzzle in our series of sudoku variations. It was kindly provided by Brainfreeze puzzles, a puzzle making company run by the mathematician Laura Taalman and the software developer Philip Riley, whose book Color Sudoku is published by Sterling Publishing.

Each of the numbers 1 to 9 must appear exactly once in each row, column, and block. In addition, adjacent cells must obey any "greater than" (>) or "less than" (<) symbol that appears on their dividing line. Note that this puzzle has no starting clues given; the greater than symbols are enough to determine a unique solution without any initial conditions at all! As an aid in solving, some cells have been shaded. Cells with a lower value than all their neighbours are blue; cells with a higher value than all their neighbours are red. Happy puzzling!

If you are stumped by last issue's puzzle, here is the solution.

For some challenging mathematical puzzles, see the NRICH puzzles from this month or last month.