A transformation sequence from word beginWord to word endWord using a dictionary wordList is a sequence of words beginWord -> s₁ -> s₂ -> ... -> sₖ such that:

• Every adjacent pair of words differs by a single letter.
• Every sᵢ for 1 <= i <= k is in wordList. Note that beginWord does not need to be in wordList.
• sₖ == endWord

Given two words, beginWord and endWord, and a dictionary wordList, return the number of words in the shortest transformation sequence from beginWord to endWord, or 0 if no such sequence exists.

Examples

Example 1

Input:  beginWord = "hit", endWord = "cog", wordList = ["hot","dot","dog","lot","log","cog"]
Output: 5

One shortest transformation sequence is "hit" -> "hot" -> "dot" -> "dog" -> cog", which is 5 words long.

Example 2

Input:  beginWord = "hit", endWord = "cog", wordList = ["hot","dot","dog","lot","log"]
Output: 0

The endWord "cog" is not in wordList, therefore there is no valid transformation sequence.

Constraints

• 1 <= beginWord.length <= 10
• endWord.length == beginWord.length
• 1 <= wordList.length <= 5000
• wordList[i].length == beginWord.length
• beginWord, endWord, and wordList[i] consist of lowercase English letters.
• beginWord != endWord
• All the words in wordList are unique.