<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> </p> <p><strong>Example 1:</strong></p> <pre> <strong>Input:</strong> ["FrontMiddleBackQueue", "pushFront", "pushBack", "pushMiddle", "pushMiddle", "popFront", "popMiddle", "popMiddle", "popBack", "popFront"] [[], [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 -> [4, 3, 2] q.popMiddle(); // return 3 -> [4, 2] q.popMiddle(); // return 4 -> [2] q.popBack(); // return 2 -> [] q.popFront(); // return -1 -> [] (The queue is empty) </pre> <p> </p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 <= val <= 10<sup>9</sup></code></li> <li>At most <code>1000</code> calls will be made to <code>pushFront</code>, <code>pushMiddle</code>, <code>pushBack</code>, <code>popFront</code>, <code>popMiddle</code>, and <code>popBack</code>.</li> </ul>