Max Stack

You have to implement a special data structure “MAX_STACK” it would be a hybrid data structure of max heap and stack. Basically, it will have all the functionality of a stack in addition to it the max stack should also give max element in a stack in O(1). you have to implement the following functions:

specialPush(value): should push the value in the stack in O(1).
specialPop( ) : should pop the last element from the stack in O(1).
specialTop( ): should give the element at the top of the stack in O(1).
specialMax( ): should give the maximum element from all the elements that are currently present in the stack in O(1).

In addition it tries to construct it only using the stack data structure.

Four types of queries denote these operations:

Type 1 : for specialPush(value) operation.
Type 2 : for specialPop( ) operation.
Type 3 : for specialTop( ) operation.
Type 4 : for specialMax( ) operation.

Input format:

The first line of input contains a single integer 'Q', denoting the number of queries.

The next 'Q' line contains one operation per line.

Each operation starts with a single positive integer representing the type of operation. 

If it is 1 then the operation is of type 1 and it is followed by a positive integer value.
If it is 2, 3, or 4 then it represents the operation of type 2, 3, and 4 respectively.

Output format :

For each operation of type 2, return an integer on a single line - the element popped from the stack, and if there is underflow i.e. there is no element in the stack then return -1.
For each operation of type 3, return an integer on a single line - the top element of the stack and if the stack is empty return -1.
For each operation of type 4, return an integer on a single line - the maximum element on the stack and if the stack is empty return -1.  

Note :

You do not need to print anything. It has already been taken care of. Just implement the given function.

Constraint :

1 <= Q <= 10^6
1 <= type <= 4
1 <= value <= 10^9

Time Limit : 1 sec