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433\. Minimum Genetic Mutation

Medium

A gene string can be represented by an 8-character long string, with choices from `'A'`, `'C'`, `'G'`, and `'T'`.

Suppose we need to investigate a mutation from a gene string `startGene` to a gene string `endGene` where one mutation is defined as one single character changed in the gene string.

*   For example, `"AACCGGTT" --> "AACCGGTA"` is one mutation.

There is also a gene bank `bank` that records all the valid gene mutations. A gene must be in `bank` to make it a valid gene string.

Given the two gene strings `startGene` and `endGene` and the gene bank `bank`, return _the minimum number of mutations needed to mutate from_ `startGene` _to_ `endGene`. If there is no such a mutation, return `-1`.

Note that the starting point is assumed to be valid, so it might not be included in the bank.

**Example 1:**

**Input:** startGene = "AACCGGTT", endGene = "AACCGGTA", bank = ["AACCGGTA"]

**Output:** 1

**Example 2:**

**Input:** startGene = "AACCGGTT", endGene = "AAACGGTA", bank = ["AACCGGTA","AACCGCTA","AAACGGTA"]

**Output:** 2

**Constraints:**

*   `0 <= bank.length <= 10`
*   `startGene.length == endGene.length == bank[i].length == 8`
*   `startGene`, `endGene`, and `bank[i]` consist of only the characters `['A', 'C', 'G', 'T']`.




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