2265\. Count Nodes Equal to Average of Subtree

Medium

Given the `root` of a binary tree, return _the number of nodes where the value of the node is equal to the **average** of the values in its **subtree**_.

**Note:**

*   The **average** of `n` elements is the **sum** of the `n` elements divided by `n` and **rounded down** to the nearest integer.
*   A **subtree** of `root` is a tree consisting of `root` and all of its descendants.

**Example 1:**

![](https://assets.leetcode.com/uploads/2022/03/15/image-20220315203925-1.png)

**Input:** root = [4,8,5,0,1,null,6]

**Output:** 5

**Explanation:**

For the node with value 4: The average of its subtree is (4 + 8 + 5 + 0 + 1 + 6) / 6 = 24 / 6 = 4.

For the node with value 5: The average of its subtree is (5 + 6) / 2 = 11 / 2 = 5.

For the node with value 0: The average of its subtree is 0 / 1 = 0.

For the node with value 1: The average of its subtree is 1 / 1 = 1.

For the node with value 6: The average of its subtree is 6 / 1 = 6.

**Example 2:**

![](https://assets.leetcode.com/uploads/2022/03/26/image-20220326133920-1.png)

**Input:** root = [1]

**Output:** 1

**Explanation:** For the node with value 1: The average of its subtree is 1 / 1 = 1.

**Constraints:**

*   The number of nodes in the tree is in the range `[1, 1000]`.
*   `0 <= Node.val <= 1000`
