Check Palindromic Array

Given an array of strings arr, the array is a palindromic array if every element is equal to its corresponding pair: the first element equals the last, the second equals the second-to-last, and so on.

If the array is not palindromic, you can try to convert it into a palindromic array by performing the following operations any number of times:

1. Take a prefix from an element's right neighbour and add it to the element as a suffix.
2. Take a suffix from an element's left neighbour and add it to the element as a prefix.

A move can take any number of characters, but every element must keep at least one character, so the number of elements never changes. Return true if arr is already palindromic or can be converted into a palindromic array with these operations, otherwise false.

Example 1

Input:  arr = ["ab","a","aa","b"]
Output: true

Shift the 3rd element's suffix "a" to the 4th element's prefix: ["ab","a","a","ab"].

Example 2

Input:  arr = ["aa","ba","a","baaa","b"]
Output: true

Shift the 2nd element's prefix "b" to the 1st element's suffix, the 4th element's suffix "aa" to the 5th element's prefix, and the 4th element's prefix "b" to the 3rd element's suffix: ["aab","a","ab","a","aab"].

Example 3

Input:  arr = ["ab","ba"]
Output: false

The characters together read "abba", a palindrome, but a palindromic array of two elements needs both elements equal, and no shift makes "ab" and "ba" equal.

Constraints

• 1 <= arr.length <= 1000
• 1 <= arr[i].length
• The total number of characters across all elements is at most 2000.
• arr[i] consists of lowercase English letters.