haskell problem 63 (brute force)

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+-- Powerful digit counts
+--
+-- Problem 63
+-- The 5-digit number, 16807=7^5, is also a fifth power. Similarly, the 9-digit number,
+-- 134217728=8^9, is a ninth power.
+--
+-- How many n-digit positive integers exist which are also an nth power?
+
+
+-- when should i stop ? (maybe stop searching when x ^ y has more than y digits)
+main = do
+    -- print (numbers)
+    print (length numbers)
+
+numbers = [x ^ y| x <- [1..200], y <- [1..x], digitCount (x ^ y) == y]
+
+digitCount :: Integer -> Integer
+digitCount n
+  | n < 10 = 1
+  | otherwise = 1 + digitCount (n `div` 10)