Balanced Binary Tree Rearrangement

You are given a list of integers representing the nodes of a binary tree. Your task is to determine whether it is possible to rearrange these nodes to form a balanced binary tree.

A balanced binary tree is one in which the depths of the two subtrees of every node differ by no more than one. In this problem, we use a related concept based on a complete binary tree. Given n nodes, the height h of a complete binary tree is computed as:

$$h = \lceil \log_{2}(n+1) \rceil - 1$$

The total number of nodes in a complete binary tree of height h is:

$$\text{complete\_nodes} = 2^{h+1} - 1$$

If the difference between complete_nodes and n is not more than \(2^{h}\), then it is possible to rearrange the nodes to form a balanced binary tree. In such a case, print Yes; otherwise, print No.

inputFormat

The first line contains a single integer n representing the number of nodes.

The second line contains n space-separated integers which represent the node values.

outputFormat

Output a single line with either Yes if the nodes can be rearranged to form a balanced binary tree, or No otherwise.

## sample

5
1 2 3 4 5

Yes