The economic crisis continues in our beloved kingdom. The king has asked the data scientists to collect the data of each inhabitant of the kingdom. The king's goal is to initiate some transactions among the inhabitants so that the crisis is mitigated.

But collecting data is itself a costly piece of work. Thus, the data scientists have decided to generate some data and run simulations on them. Initially, they would like to consider a simple model in which $\textbf N$ inhabitants are labelled from $\textbf 1$ to $\textbf N$ and the $i^{th}$ individual will have $\textbf i$ amount of money. Your task is to decide whether it would be possible to distribute the wealth equally across the kingdom if any person in the kingdom can make transactions with any other person in the kingdom. A person can make as many transactions as he wants to others.

Input

The only line of input will have an integer $\textbf N$$(1\leq N \leq 10^{18})$, the number of inhabitants in the kingdom.

Output

For each of the cases, output Yes, if it is possible to distribute the money equally, or No otherwise.

Sample

Input

Output

1

Yes

Since the kingdom has only one person, we will get all the wealth he has.