A min-max heap is a data structure that supports both deleteMin and deleteMax in O(log N) per operation. The structure is identical to a binary heap, but the heap-order property is that for any node, X, at even depth, the element stored at X is smaller than the parent but larger than the grandparent (where this makes sense), and for any node X at odd depth, the element stored at X is larger than the parent but smaller than the grandparent (see figure 1). 6 81 87 14 17 71 80 12 25 20 52 28 78 31 42 31 59 16 24 79 63 18 19 32 13 15 48 Figure 1: A min-max heap. Using an array to represent the min-max heap structure (in the same way as for min heap or max heap), implement the following operations.

1. buildHeap : Builds a min-max heap from a list of naturals read from standard input.

2. findMin and findMax : Returns the minimum (resp the maximum) element.

3. insertHeap : Inserts a new element into the min-max heap.

4. deleteMin and deleteMax : Deletes the minimum (resp the maximum) element.

(c++ please)