# ---
# title: 1609. Even Odd Tree
# id: problem1609
# author: Tian Jun
# date: 2020-10-31
# difficulty: Medium
# categories: Tree
# link: <https://leetcode.com/problems/even-odd-tree/description/>
# hidden: true
# ---
# 
# 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:**
# 
# **![](https://assets.leetcode.com/uploads/2020/09/15/sample_1_1966.png)**
# 
#     
#     
#     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:**
# 
# **![](https://assets.leetcode.com/uploads/2020/09/15/sample_2_1966.png)**
# 
#     
#     
#     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 the level 2 must be in strictly increasing order, so the tree is not Even-Odd.
#     
# 
# **Example 3:**
# 
# ![](https://assets.leetcode.com/uploads/2020/09/22/sample_1_333_1966.png)
# 
#     
#     
#     Input: root = [5,9,1,3,5,7]
#     Output: false
#     Explanation: Node values in the level 1 should be even integers.
#     
# 
# **Example 4:**
# 
#     
#     
#     Input: root = [1]
#     Output: true
#     
# 
# **Example 5:**
# 
#     
#     
#     Input: root = [11,8,6,1,3,9,11,30,20,18,16,12,10,4,2,17]
#     Output: true
#     
# 
# 
# 
# **Constraints:**
# 
#   * The number of nodes in the tree is in the range `[1, 105]`.
#   * `1 <= Node.val <= 106`
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
