Word statistics with streams

Read one line of text and summarise its words using streams and collectors.

A word is a maximal run of letters A–Z/a–z; everything else separates words. Convert every word to lower case before processing. The line may be empty or contain no letters at all.

Print exactly four lines:

1. Words: and the number of words;
2. Distinct: and the distinct words in alphabetical order, as [w1, w2, …] ([] when there are none);
3. Longest: and the longest word — if several share the maximum length, the alphabetically first — or none;
4. By length: and a map from word length to number of words, keys in increasing order, printed with the map's toString (e.g. {3=5, 5=1}, or {}).

Input:
The cat saw the other cat.

Output:
Words: 6
Distinct: [cat, other, saw, the]
Longest: other
By length: {3=5, 5=1}

Hint: line.split("[^A-Za-z]+") can produce an empty first element, so filter it out.