A mergeable heap supports operations insert(k, x), remove(k), unionWith(h), and min(), where the unionWith(h) operation performs a union of the mergeable heap h with the present one, destroying the old versions of both, and min() returns the element with minimum key. Describe a implementation of a mergeable heap that achieves O(log n) performance for all its operations. For simplicity, you may assume that all keys in existing mergeable heaps are distinct, although this is not strictly necessary.