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CSES Problem Set

Weird Algorithm


Task | Statistics


CSES - 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
Example

Input:
3

Output:
3 10 5 16 8 4 2 1