Design a max stack that supports push, pop, top, peekMax and popMax.

1. push(x) -- Push element x onto stack.
2. pop() -- Remove the element on top of the stack and return it.
3. top() -- Get the element on the top.
4. peekMax() -- Retrieve the maximum element in the stack.
5. popMax() -- Retrieve the maximum element in the stack, and remove it. If you find more than one maximum elements, only remove the top-most one.

Example 1:

MaxStack stack = new MaxStack();
stack.push(5); 
stack.push(1);
stack.push(5);
stack.top(); -
>
 5
stack.popMax(); -
>
 5
stack.top(); -
>
 1
stack.peekMax(); -
>
 5
stack.pop(); -
>
 1
stack.top(); -
>
 5

Note:

1. -1e7 < = x < = 1e7
2. Number of operations won't exceed 10000.
3. The last four operations won't be called when stack is empty.

class MaxStack {

    Stack<Integer> stack;
    Stack<Integer> maxStack;

    /** initialize your data structure here. */
    public MaxStack() {
        stack = new Stack<>();
        maxStack = new Stack<>();
    }

    public void push(int x) {
        stack.push(x);
        if (maxStack.isEmpty() || x > maxStack.peek()){
            maxStack.push(x);
        }
        else{
            maxStack.push(maxStack.peek());
        }
    }

    public int pop() {
        maxStack.pop();

        return stack.pop();
    }

    public int top() {
        return !stack.isEmpty() ? stack.peek() : -1;
    }

    public int peekMax() {
        return !maxStack.isEmpty() ? maxStack.peek() : -1;
    }

    public int popMax() {
        int curMax = maxStack.peek();
        Stack<Integer> temp = new Stack<>();

        while (!stack.isEmpty() && stack.peek() != curMax){
            //System.out.println("cur max: " + curMax + " stack top: " + stack.peek());
            maxStack.pop();
            temp.push(stack.pop());
        }

        stack.pop();
        maxStack.pop();

        int newMax = !maxStack.isEmpty() ? maxStack.peek() : Integer.MIN_VALUE;
        while (!temp.isEmpty()){
            int val = temp.pop();
            stack.push(val);
            newMax = Math.max(newMax, val);
            maxStack.push(newMax);
        }

        return curMax;
    }
}

/**
 * Your MaxStack object will be instantiated and called as such:
 * MaxStack obj = new MaxStack();
 * obj.push(x);
 * int param_2 = obj.pop();
 * int param_3 = obj.top();
 * int param_4 = obj.peekMax();
 * int param_5 = obj.popMax();
 */