Layers in a Rug

Write a function that counts how many concentric layers a rug has.

Examples

countLayers([
  "AAAA",
  "ABBA",
  "AAAA"
]) ➞ 2

countLayers([
  "AAAAAAAAA",
  "ABBBBBBBA",
  "ABBAAABBA",
  "ABBBBBBBA",
  "AAAAAAAAA"
]) ➞ 3

countLayers([
  "AAAAAAAAAAA",
  "AABBBBBBBAA",
  "AABCCCCCBAA",
  "AABCAAACBAA",
  "AABCADACBAA",
  "AABCAAACBAA",
  "AABCCCCCBAA",
  "AABBBBBBBAA",
  "AAAAAAAAAAA"
]) ➞ 5

Notes

• Multiple layers can share the same component so count them separately (example #2).
• Layers will be horizontally and vertically symmetric.
• There will be at least one layer for each rug.