Weird Algorithm

Consider an algorithm that takes as input a positive integer $nn$. If $nn$ is even, the algorithm divides it by two, and if $nn$ is odd, the algorithm multiplies it by three and adds one. The algorithm repeats this, until $nn$ is one. For example, the sequence for $n=3n=3$ is as follows: $$3\to 10\to 5\to 16\to 8\to 4\to 2\to 13\; \backslash rightarrow\; 10\; \backslash rightarrow\; 5\; \backslash rightarrow\; 16\; \backslash rightarrow\; 8\; \backslash rightarrow\; 4\; \backslash rightarrow\; 2\; \backslash rightarrow\; 1$$ Your task is to simulate the execution of the algorithm for a given value of $nn$.

Input

The only input line contains an integer $nn$.

Output

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