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In a binary tree, the root node is at depth 0, and children of each depth k node are at depth k+1.

Two nodes of a binary tree are cousins if they have the same depth, but have different parents.

We are given the root of a binary tree with unique values, and the values x and y of two different nodes in the tree.

Return true if and only if the nodes corresponding to the values x and y are cousins.

Example 1:

1

Input: root = [1,2,3,4], x = 4, y = 3
Output: false

Example 2:

2

Input: root = [1,2,3,null,4,null,5], x = 5, y = 4
Output: true

Example 3:

3

Input: root = [1,2,3,null,4], x = 2, y = 3
Output: false

Note:

  • The number of nodes in the tree will be between 2 and 100.
  • Each node has a unique integer value from 1 to 100.