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].