Order by Length First

Graded lexicographic order (grlex order for short) is a way of ordering words that:

1. First orders words by length.
2. Then orders words of the same size by their dictionary order.

For example, in grlex order:

• "tray" < "trapped" since "tray" has length 4 while "trapped" has length 7.
• "trap" < "tray" since both have length 4, but "trap" comes before "tray" in the dictionary.

Given a list of words, return that list in grlex order.

Examples

make_grlex(["small", "big"]) ➞ ["big", "small"]

make_grlex(["cat", "ran", "for", "the", "rat"]) ➞ ["cat", "for", "ran", "rat", "the"]

make_grlex(["this", "is", "a", "small", "test"]) ➞ ["a", "is", "test", "this", "small"]

Notes

N/A