Weird Algorithm

• Time limit: 1.00 s
• Memory limit: 512 MB

Consider an algorithm that takes as input a positive integer $n$. If $n$ is even, the algorithm divides it by two, and if $n$ is odd, the algorithm multiplies it by three and adds one. The algorithm repeats this, until $n$ is one. For example, the sequence for $n=3$ is as follows:
\[ 3 \rightarrow 10 \rightarrow 5 \rightarrow 16 \rightarrow 8 \rightarrow 4 \rightarrow 2 \rightarrow 1\]
Your task is to simulate the execution of the algorithm for a given value of $n$.

Input

The only input line contains an integer $n$.

Output

Print a line that contains all values of $n$ during the algorithm.

Constraints

• $1 \le n \le 10^6$
  

Example

Input:
3

Output:
3 10 5 16 8 4 2 1