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# 1609. Even Odd Tree

<https://leetcode.com/problems/even-odd-tree>

## Description

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`

## ac

```java
```