Even Odd Tree

A binary tree is named Even-Odd if it meets the following conditions:

The root of the binary tree is at level index 0, its children are at level index 1, their children are at level index 2, etc.
For every even-indexed level, all nodes at the level have odd integer values in strictly increasing order from left to right.
For every odd-indexed level, all nodes at the level have even integer values in strictly decreasing order from left to right.

Given the root of a binary tree, return true if the binary tree is Even-Odd, otherwise return false.

Example 1

          1
        /   \
      10     4
     /      / \
    3      7   9
   / \    /     \
 12   8  6       2

Inputroot = [1,10,4,3,null,7,9,12,8,6,null,null,2]

Outputtrue

Levels 0 and 2 contain odd values in strictly increasing order, and levels 1 and 3 contain even values in strictly decreasing order.

Example 2

Inputroot = [5,4,2,3,3,7]

Outputfalse

Level 2 contains values [3, 3, 7], which are not in strictly increasing order.

Constraints