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 `start` to a gene string `end` 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 `start` and `end` and the gene bank `bank`, return the minimum number of mutations needed to mutate from `start` to `end`. 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: start = "AACCGGTT", end = "AACCGGTA", bank = ["AACCGGTA"]
    Output: 1

Example 2:

    Input: start = "AACCGGTT", end = "AAACGGTA", bank = ["AACCGGTA","AACCGCTA","AAACGGTA"]
    Output: 2

Example 3:

    Input: start = "AAAAACCC", end = "AACCCCCC", bank = ["AAAACCCC","AAACCCCC","AACCCCCC"]
    Output: 3

Constraints:

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