Directional Word Cages: Quadrata

This puzzle is very similar to the last one, except this time we allow ourselves to consider which letters come before which letter is the alphabet.  Arrows always point towards the letter that comes first, and lack of an arrow means that the letters must be the same.  These clues make this puzzle a bit easier than the last Word Cage even though there are fewer clues, though the strategies needed here might feel quite different.

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Solution.