Add the bottles problem

.github/bottles.py

@@ -0,0 +1,39 @@
+import unittest
+
+from collections import Counter
+from functools import cache
+
+
+@cache
+def howmany(bottles: tuple):
+    if len(bottles) == 1:
+        return bottles[0] + 1
+
+    def sub(ix):
+        bottles1 = sorted((jb - (jx == ix) for jx, jb in enumerate(bottles)))
+        return tuple(b for b in bottles1 if b)
+
+    return sum(howmany(sub(i)) for i in range(len(bottles))) + 1
+
+
+def main(letters):
+    c = sorted(Counter(letters).values())
+    return howmany(tuple(c)) - 1
+
+
+class TestHowMany(unittest.TestCase):
+    def test_howmany(self):
+        self.assertEqual(howmany((5,)), 6)
+        self.assertEqual(howmany((1, 1)), 5)
+        self.assertEqual(howmany((1, 1, 1)), 16)
+
+
+class TestMain(unittest.TestCase):
+    def test_main(self):
+        self.assertEqual(main("ab"), 4)
+        self.assertEqual(main("abc"), 15)
+        self.assertEqual(main("aaaaa"), 5)
+
+
+if __name__ == "__main__":
+    print(main(input().strip()))