Word Frequency Counter

Given a string of text that may contain punctuation, numbers, and spaces, your task is to count the occurrences of each word in the string. Only alphabetical characters (a-z and A-Z) are considered part of a word. All words should be treated as case-insensitive (i.e. converted to lowercase).

Details:

• Non-alphabetical characters (such as punctuation and numbers) should be treated as delimiters.
• Words are sequences of alphabetical characters.
• The output should list each word and its count, with the words sorted in lexicographical (alphabetical) order.

Mathematical Formulation:

Let \( S \) be the input string. For each word \( w \) extracted from \( S \), let \( f(w) \) denote its frequency. The output is the set \( \{(w, f(w)) \mid w \in W \} \) where \( W \) is the set of distinct words from \( S \), sorted in ascending order.

inputFormat

The input is a string read from standard input (stdin). The string may span multiple lines.

outputFormat

For each distinct word in the input, output a line containing the word in lowercase, a single space, and its frequency count. The words must appear in lexicographical (alphabetical) order. Output to standard output (stdout).

## sample

Hello, hello! How are you? I hope you are well. Well, well, well...

are 2
hello 2
how 1
i 1
hope 1
well 4
you 2

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