Group Words by Length

Given a list of words, your task is to group them by their length. For each word \(w\) in the input, let \(|w|\) be the length of the word. You must then output each group on a separate line. The words in each group should be sorted in alphabetical order, and the groups must be printed in increasing order of the word lengths.

Example:

Input:  apple bat banana ape grape kiwi
Output:
3: ape bat
4: kiwi
5: apple grape
6: banana

inputFormat

The input is given via standard input (stdin) as a single line containing space-separated words.

outputFormat

For each distinct word length, output a line in the following format: length: word1 word2 .... The words in each line should be sorted alphabetically, and the lines should be ordered by increasing word length.

## sample

apple bat banana ape grape kiwi

3: ape bat
4: kiwi
5: apple grape
6: banana

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