Design Front Middle Back Queue
<p>Design a queue that supports <code>push</code> and <code>pop</code> operations in the front, middle, and back.</p>

<p>Implement the <code>FrontMiddleBack</code> class:</p>

<ul>
	<li><code>FrontMiddleBack()</code> Initializes the queue.</li>
	<li><code>void pushFront(int val)</code> Adds <code>val</code> to the <strong>front</strong> of the queue.</li>
	<li><code>void pushMiddle(int val)</code> Adds <code>val</code> to the <strong>middle</strong> of the queue.</li>
	<li><code>void pushBack(int val)</code> Adds <code>val</code> to the <strong>back</strong> of the queue.</li>
	<li><code>int popFront()</code> Removes the <strong>front</strong> element of the queue and returns it. If the queue is empty, return <code>-1</code>.</li>
	<li><code>int popMiddle()</code> Removes the <strong>middle</strong> element of the queue and returns it. If the queue is empty, return <code>-1</code>.</li>
	<li><code>int popBack()</code> Removes the <strong>back</strong> element of the queue and returns it. If the queue is empty, return <code>-1</code>.</li>
</ul>

<p><strong>Notice</strong> that when there are <b>two</b> middle position choices, the operation is performed on the <strong>frontmost</strong> middle position choice. For example:</p>

<ul>
	<li>Pushing <code>6</code> into the middle of <code>[1, 2, 3, 4, 5]</code> results in <code>[1, 2, <u>6</u>, 3, 4, 5]</code>.</li>
	<li>Popping the middle from <code>[1, 2, <u>3</u>, 4, 5, 6]</code> returns <code>3</code> and results in <code>[1, 2, 4, 5, 6]</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong>
[&quot;FrontMiddleBackQueue&quot;, &quot;pushFront&quot;, &quot;pushBack&quot;, &quot;pushMiddle&quot;, &quot;pushMiddle&quot;, &quot;popFront&quot;, &quot;popMiddle&quot;, &quot;popMiddle&quot;, &quot;popBack&quot;, &quot;popFront&quot;]
[[], [1], [2], [3], [4], [], [], [], [], []]
<strong>Output:</strong>
[null, null, null, null, null, 1, 3, 4, 2, -1]

<strong>Explanation:</strong>
FrontMiddleBackQueue q = new FrontMiddleBackQueue();
q.pushFront(1);   // [<u>1</u>]
q.pushBack(2);    // [1, <u>2</u>]
q.pushMiddle(3);  // [1, <u>3</u>, 2]
q.pushMiddle(4);  // [1, <u>4</u>, 3, 2]
q.popFront();     // return 1 -&gt; [4, 3, 2]
q.popMiddle();    // return 3 -&gt; [4, 2]
q.popMiddle();    // return 4 -&gt; [2]
q.popBack();      // return 2 -&gt; []
q.popFront();     // return -1 -&gt; [] (The queue is empty)
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= val &lt;= 10<sup>9</sup></code></li>
	<li>At most&nbsp;<code>1000</code>&nbsp;calls will be made to&nbsp;<code>pushFront</code>,&nbsp;<code>pushMiddle</code>,&nbsp;<code>pushBack</code>, <code>popFront</code>, <code>popMiddle</code>, and <code>popBack</code>.</li>
</ul>
Design; Queue; Array; Linked List; Data Stream
class FrontMiddleBackQueue:
    def __init__(self):
        self.q1 = deque()
        self.q2 = deque()

    def pushFront(self, val: int) -> None:
        self.q1.appendleft(val)
        self.rebalance()

    def pushMiddle(self, val: int) -> None:
        self.q1.append(val)
        self.rebalance()

    def pushBack(self, val: int) -> None:
        self.q2.append(val)
        self.rebalance()

    def popFront(self) -> int:
        if not self.q1 and not self.q2:
            return -1
        if self.q1:
            val = self.q1.popleft()
        else:
            val = self.q2.popleft()
        self.rebalance()
        return val

    def popMiddle(self) -> int:
        if not self.q1 and not self.q2:
            return -1
        if len(self.q1) == len(self.q2):
            val = self.q1.pop()
        else:
            val = self.q2.popleft()
        self.rebalance()
        return val

    def popBack(self) -> int:
        if not self.q2:
            return -1
        val = self.q2.pop()
        self.rebalance()
        return val

    def rebalance(self):
        if len(self.q1) > len(self.q2):
            self.q2.appendleft(self.q1.pop())
        if len(self.q2) > len(self.q1) + 1:
            self.q1.append(self.q2.popleft())


# Your FrontMiddleBackQueue object will be instantiated and called as such:
# obj = FrontMiddleBackQueue()
# obj.pushFront(val)
# obj.pushMiddle(val)
# obj.pushBack(val)
# param_4 = obj.popFront()
# param_5 = obj.popMiddle()
# param_6 = obj.popBack()
