The $$$n^2 + 1$$$ Conjecture
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

While walking around the university, waiting for the olympiad to begin, you accidentally came across an open door to one of the classrooms.

It turned out to be a laboratory for multiplying and dividing positive integers.

On one of the laboratory boards, the following hypothesis was written, left by one of the lab assistants:

Take any positive integer $$$n$$$.

While the given number is not equal to one, perform the following steps:

  1. If $$$n$$$ is even, divide the number by $$$2$$$.
  2. If $$$n$$$ is odd, square the number and add one.

I know for which numbers this process terminates in a finite number of steps. Do you?

So you started wondering how, for a given number $$$n$$$, to determine whether it can be transformed into one in a finite number of steps.

Input

The only line contains one integer $$$n$$$ $$$(1 \le n \le 10^9)$$$ — the number for which it is required to determine whether it is transformed into one in a finite number of steps of the described process.

Output

Print one line: "YES" if the given number $$$n$$$ is transformed into one in a finite number of steps, and "NO" otherwise.

It is guaranteed that the answer always exists and is unique.

Examples
Input
1
Output
YES
Input
17
Output
NO
Input
4
Output
YES
Note

Example 1. For $$$n = 1$$$, the number is already equal to one, so no steps of the process need to be performed. The answer is "YES".

Example 2. For $$$n = 17$$$, the process begins as follows: $$$17 \to 290 \to 145 \to 21026 \to \ldots$$$ It can be proved that one will never be obtained for this sequence, and the answer — "NO".

Example 3. For $$$n = 4$$$, the process looks like this: $$$4 \to 2 \to 1$$$. One is obtained in two steps. The answer is "YES".