# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right

def traverse(root) -> list[list[int]]:
    nodes: list[list[int]] = []

    def helper(node: Optional[TreeNode], level: int):
        if node:
            if nodes.__len__() == level:
                nodes.append([])

        if node.left:
            nodes[level].append(node.left.val)
            helper(node.left, level + 1)

        if node.right:
            nodes[level].append(node.right.val)
            helper(node.right, level + 1)

    helper(root, 0);

    return nodes


class Solution:
    def isEvenOddTree(self, root: Optional[TreeNode]) -> bool:
        nodes: list[list[int]] = []

        if root:
            nodes = [[root.val]] + traverse(root)
            nodes.pop()
        else:
            return False

        for i in range(nodes.__len__()):
            level: list[int] = nodes[i]

            if i % 2:
                if level[0] % 2:
                    return False
                for j in range(level.__len__() - 1):
                    if level[j] <= level[j + 1] or level[j] % 2 or level[j + 1] % 2:
                        return False
            else:
                if level[0] % 2 == 0:
                    return False
                for j in range(level.__len__() - 1):
                    if level[j] >= level[j + 1] or level[j] % 2 == 0 or level[j + 1] % 2 == 0:
                        return False
        return True