Based on the method of this problem, write a function to calculate the letter distance for a set of words and then return the sorted set of words based on their distances, in ascending order. However, their distances will now be normalized by the number of characters in each word. For example, if

 str_arr = {'jazz','cab','tree'}

then

 d = [(9+25+0)/4, (2+1)/3, (2+13+0)/4] = [34/4, 3/3, 15/4] = [8.5, 1, 3.75]

which would result in the following sorted order:

 str_arr_sort = {'cab','tree','jazz'}

Remember that the method is case insensitive. See the test suite for examples.