Two Stack Queue

Building a Queue with Two Stacks: A Challenge in Engineering Elegance

The Objective: Queue with Stacks

In this challenge, your task is to implement a queue using two stacks. While many programming languages offer queues through arrays or lists, we're restricting our approach to only utilize stacks.

The end result should behave like this:

const tsq = new TwoStackQueue();
tsq.push(1);
tsq.push(2);
tsq.pop();  // Should return 1
tsq.pop();  // Should return 2

The Blueprint: Visualizing the Mechanics

Imagine having two stacks that work in harmony to simulate a queue. These stacks are like two components of a complex machine, each with its own specific role.

Constraints and Expectations

Let's clarify the rules of the game:

• Number of Operations: The maximum number of operations won't exceed 100,000.
• Value Ranges: The elements you push onto the stack will range between -1,000,000,000 and 1,000,000,000.
• Time Complexity for Push: If the pop operation has a time complexity of O(n), then the push operation should be O(1). Otherwise, the time complexity for push should be O(n).
• Time Complexity for Pop: If the push operation has a time complexity of O(n), then the pop operation should be O(1). Otherwise, it should be O(n).
• Space Complexity: Expected to be O(n).

```javascript
class TwoStackQueue {
  def __init__(self):
    self.inbox = []
    self.outbox = []
  }

  def push():
    # fill in
    return
  
  def pop():
    # fill in
    return
```