You are given a doubly linked list, which contains nodes that have a next pointer, a previous pointer, and an additional child pointer. This child pointer may or may not point to a separate doubly linked list, also containing these special nodes. These child lists may have one or more children of their own, and so on, to produce a multilevel data structure as shown in the example below.

Given the `head` of the first level of the list, flatten the list so that all the nodes appear in a single-level, doubly linked list. Let `curr` be a node with a child list. The nodes in the child list should appear after `curr` and before `curr.next` in the flattened list.

Return the `head` of the flattened list. The nodes in the list must have all of their child pointers set to `null`.

Example 1:

    Input: head = [1,2,3,4,5,6,null,null,null,7,8,9,10,null,null,11,12]
    Output: [1,2,3,7,8,11,12,9,10,4,5,6]
    Explanation: The multilevel linked list in the input is shown.
    After flattening the multilevel linked list it becomes:

Example 2:

    Input: head = [1,2,null,3]
    Output: [1,3,2]
    Explanation: The multilevel linked list in the input is shown.
    After flattening the multilevel linked list it becomes:

Example 3:

    Input: head = []
    Output: []
    Explanation: There could be empty list in the input.

Constraints:

- The number of Nodes will not exceed `1000`.
- `1 <= Node.val <= 105`

How the multilevel linked list is represented in test cases:

We use the multilevel linked list from Example 1 above:

     1---2---3---4---5---6--NULL
             |
             7---8---9---10--NULL
                 |
                 11--12--NULL

The serialization of each level is as follows:

    [1,2,3,4,5,6,null]
    [7,8,9,10,null]
    [11,12,null]

To serialize all levels together, we will add nulls in each level to signify no node connects to the upper node of the previous level. The serialization becomes:

    [1,    2,    3, 4, 5, 6, null]
                 |
    [null, null, 7,    8, 9, 10, null]
                       |
    [            null, 11, 12, null]

Merging the serialization of each level and removing trailing nulls we obtain:

    [1,2,3,4,5,6,null,null,null,7,8,9,10,null,null,11,12]