Given the `root` of a binary tree, construct a 0-indexed `m x n` string matrix `res` that represents a formatted layout of the tree. The formatted layout matrix should be constructed using the following rules:

- The height of the tree is `height` and the number of rows `m` should be equal to `height + 1`.
- The number of columns `n` should be equal to `2height+1 - 1`.
- Place the root node in the middle of the top row (more formally, at location `res[0][(n-1)/2]`).
- For each node that has been placed in the matrix at position `res[r][c]`, place its left child at `res[r+1][c-2height-r-1]` and its right child at `res[r+1][c+2height-r-1]`.
- Continue this process until all the nodes in the tree have been placed.
- Any empty cells should contain the empty string `""`.

Return the constructed matrix `res`.

Example 1:

    Input: root = [1,2]
    Output:
    [["","1",""],
     ["2","",""]]

Example 2:

    Input: root = [1,2,3,null,4]
    Output:
    [["","","","1","","",""],
     ["","2","","","","3",""],
     ["","","4","","","",""]]

Constraints:

- The number of nodes in the tree is in the range `[1, 210]`.
- `-99 <= Node.val <= 99`
- The depth of the tree will be in the range `[1, 10]`.