Shortest Transformation Sequence

You are given a begin_word, an end_word, and a dictionary word_list. Find the length of the shortest transformation sequence from begin_word to end_word, where:

• Each step changes exactly one letter.
• Every intermediate word produced (including end_word) must exist in word_list.
• begin_word does not need to be in word_list.

Return the number of words in the shortest such sequence (including both begin_word and end_word), or 0 if no such sequence exists.

Example 1

Input: begin_word = "hit", end_word = "cog", word_list = ["hot","dot","dog","lot","log","cog"]

Output: 5 — one shortest sequence is "hit" -> "hot" -> "dot" -> "dog" -> "cog".

Example 2

Input: begin_word = "hit", end_word = "cog", word_list = ["hot","dot","dog","lot","log"]

Output: 0 — "cog" is not in word_list, so no sequence can end there.

Constraints

• 1 <= begin_word.length <= 10
• end_word.length == begin_word.length
• All words consist of lowercase English letters and have the same length.
• 1 <= word_list.length <= 5000, all words distinct.