Futoshiki 5x5 #1 Very Difficult

Rules for playing online puzzle Futoshiki 5x5 #1 Very Difficult (Futoshiki, Hutosiki, Hutoshiki):

There are a few lesser known number placement puzzles that can scratch your head-spinning itch if you're a Sudoku fan: Futoshiki and Beehive Hidato.

Futoshiki will seem pretty familiar since the row and column rules from Sudoku are in effect.
But you have an additional placement rule to consider: icons smaller or larger than the grid, which indicate where to place lower or higher numbers in the grid.

(Futoshiki translates to "not equal to" in Japanese.)