Kata

The digit root of a number (dr) is the sum of the digits of a number. For example, the integer 749, has a digit root equals to 20.

In effect: 7 + 4 + 9 = 20.

We define here the deeper square double digit root of an integer n, (dsddr), the sum of the squares of every digit of the digit root of n.

The dsddr of 749 will be 4: 2² + 0² = 4

We define the function f, like:

f(n) = dr(n) + dsddr(n) 

Now we receive two arrays of positive integers, arr1 , arr2 of different lengths. They have common elements. The task is to output an array, res, with the common elements occurring once and sorted by their corresponding value of f in descending order. If there is a coincidence in the value of f(res[i]), the lowest number goes first.

Example:

arr1 = [5, 56, 28, 35, 12, 27, 64, 99, 18, 31, 14, 6]
arr2 = [28, 17, 31, 63, 64, 5, 18, 17, 95, 56, 37, 5, 28, 16]

The common elements of arr1 and arr2 are: [64, 5, 18, 56, 28, 31]

The table for their corresponding value of f is:

n        f(n)
64        11
 5        30
18        90
56        13
28        11
31        20

So the output will be: [18, 5, 31, 56, 28, 64]

You do not have to worry about the inputs, arr1 and arr2, will be always valid arrays and all of their terms, positive integers.

Features of the random tests:

lengths of arrays for the input up to 500.000.
The values of the integers between 1 and 1.500.000
Amount of tests almost 150

See more examples in the Example tests