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This problem was asked by Amazon.

Implement a stack API using only a heap. A stack implements the following methods:

• push(item), which adds an element to the stack
• pop(), which removes and returns the most recently added element (or throws an error if there is nothing on the stack)

Recall that a heap has the following operations:

• push(item), which adds a new key to the heap
• pop(), which removes and returns the max value of the heap