# 232 Implement Queue using Stacks

Implement the following operations of a queue using stacks.

* push(x) -- Push element x to the back of queue.
* pop() -- Removes the element from in front of queue.
* peek() -- Get the front element.
* empty() -- Return whether the queue is empty.

**Notes:**

* You must use only standard operations of a stack -- which means only push to top, peek/pop from top, size, and is empty operations are valid.
* Depending on your language, stack may not be supported natively. You may simulate a stack by using a list or deque (double-ended queue), as long as you use only standard operations of a stack.
* You may assume that all operations are valid (for example, no pop or peek operations will be called on an empty queue).

**The Idea:** Maintain two stacks: one that will empty itself in reverse to the second stack, only when the second stack is empty.

**Complexity:** `push()`- O(1), `pop()` - amortized O(1), `peek()` - amortized O(1), `empty()` - O(1). We have constant amortized complexity because the amount of pushes will always be equal to the number pops, and the while loops ensure that future operations of `pop`or `peek` will be available in O(1) time.

```python
class MyQueue:

    def __init__(self):
        """
        Initialize your data structure here.
        """
        self.s1, self.s2 = [], []

    def push(self, x):
        """
        Push element x to the back of queue.
        :type x: int
        :rtype: void
        """
        self.s1.append(x)

    def pop(self):
        """
        Removes the element from in front of queue and returns that element.
        :rtype: int
        """
        if len(self.s2) == 0:
            self._emptys1()
        return self.s2.pop()

    def peek(self):
        """
        Get the front element.
        :rtype: int
        """
        if len(self.s2) == 0:
            self._emptys1()
        return self.s2[-1]

    def empty(self):
        """
        Returns whether the queue is empty.
        :rtype: bool
        """
        return len(self.s1) == 0 and len(self.s2) == 0

    def _emptys1(self):
        while not len(self.s1) == 0:
            self.s2.append(self.s1.pop())


# Your MyQueue object will be instantiated and called as such:
# obj = MyQueue()
# obj.push(x)
# param_2 = obj.pop()
# param_3 = obj.peek()
# param_4 = obj.empty()
```


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