Greater-Than Sudoku

Greater-Than Sudoku is a Sudoku variant where the usual problem is replaced by specifying the comparison between the cells of the grid.

Other names for Greater-Than Sudoku are: Hikaku, Comparison Sudoku, Compdoku and probably several others. We do not know who invented Greater-Than Sudoku or where it was first published.
Similar types of puzzles: Futoshiki, Minarizumu, Sudoku.
Rules: In each cell of the NxN grid, enter a number in the range 1–N. Each number must appear exactly once in each row, column, and block.
Additional rules: A “>” between two cells indicates that the number in the cell pointed to by the tip is lower than the other cell.