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:

    Input: root = [1,10,4,3,null,7,9,12,8,6,null,null,2]
    Output: true
    Explanation: The node values on each level are:
    Level 0: [1]
    Level 1: [10,4]
    Level 2: [3,7,9]
    Level 3: [12,8,6,2]
    Since levels 0 and 2 are all odd and increasing and levels 1 and 3 are all even and decreasing, the tree is Even-Odd.

Example 2:

    Input: root = [5,4,2,3,3,7]
    Output: false
    Explanation: The node values on each level are:
    Level 0: [5]
    Level 1: [4,2]
    Level 2: [3,3,7]
    Node values in level 2 must be in strictly increasing order, so the tree is not Even-Odd.

Example 3:

    Input: root = [5,9,1,3,5,7]
    Output: false
    Explanation: Node values in the level 1 should be even integers.

Constraints:

- The number of nodes in the tree is in the range `[1, 105]`.
- `1 <= Node.val <= 106`