# Digits Doublets

...'And as for YOU,' she went on, turning fiercely upon the Red Queen, whom she considered as the cause of all the mischief--but the Queen was no longer at her side--she had suddenly dwindled down to the size of a little doll, and was now on the table, merrily running round and round after her own shawl, which was trailing behind...

The Robots like using digits more than letters, so we’ve changed the rules a little. You are given the list of numbers with exactly the same length and you must find the shortest chain of numbers to link the first number to the last like you would with the words.

For Example. There is a list [123, 991, 323, 321, 329, 121, 921, 125, 999]. The shortest way from the first to the last is: 123 ⇒ 121 ⇒ 921 ⇒ 991 ⇒ 999

You should write a function that receives a list of numbers (positive integers) and returns the shortest route as a list of numbers.

Input: Numbers as a list of integers.

Output: The shortest chain from the first to the last number as a list of integers.

Example:

```checkio([123, 991, 323, 321, 329, 121, 921, 125, 999]) == [123, 121, 921, 991, 999]
checkio([111, 222, 333, 444, 555, 666, 121, 727, 127, 777]) == [111, 121, 127, 727, 777]
checkio([456, 455, 454, 356, 656, 654]) == [456, 454, 654]  # or [456, 656, 654]
```

How it is used: This task is like pathfinding for numbers. It shows how many things in this world can be represented with mathematics, even words.

Precondition: Numbers have the same length
∀ x ∈ numbers : 100 ≤ x < 1000

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