Top Heavy Number Place

Rules: Fill the grid with digits 1-5 (1-4 for the example) so that each digits appears exactly once in every row/column. Where the digits adjoin vertically, the upper digit must be bigger.

Background: A Japanese Puzzle Championship puzzle from 2001 (1oth JPC), you can see the original page. I made this puzzle first time for OAPC 4 in as part of Matchmaker Structure. Then I used this idea in Matchmaker part of 18th WPC. So this type appeared in Tetsuya Nishio Cup The JNPC (2009) too. Probably I got from the name of puzzle. In 2010, the puzzle showed up again in Polish Puzzle Competition. I am not sure whether it was used or not in 19th WPC. And finally Vladimir transformed this type to a sudoku variant (Top Heavy Sudoku), very brilliant idea!

Example:

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