{-# OPTIONS -Wall #-}

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-- Only need to keep track of the minimum element.
type PQ a = (Maybe a,Int)

-- Creates a new priority queue.
-- Time complexity: O(1).
empty :: PQ a
empty = (Nothing,0)

-- Inserts an element.
-- Time complexity: O(1).
insert :: Ord a => a -> PQ a -> PQ a
insert e1 (me,s) = (Just $ maybe e1 (min e1) me, s+1)

-- Returns the minimum if there is one, else nothing.
-- Time complexity: O(1).
findMin :: PQ a -> Maybe a
findMin = fst

-- Returns the size.
-- Time complexity: O(1).
size :: PQ a -> Int
size = snd

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