Score : $300$ points

Problem Statement

We define sequences $S_n$ as follows.

• $S_1$ is a sequence of length $1$ containing a single $1$.
• $S_n$ ($n$ is an integer greater than or equal to $2$) is a sequence obtained by concatenating $S_{n-1}$, $n$, $S_{n-1}$ in this order.

For example, $S_2$ and $S_3$ is defined as follows.

• $S_2$ is a concatenation of $S_1$, $2$, and $S_1$, in this order, so it is $1,2,1$.
• $S_3$ is a concatenation of $S_2$, $3$, and $S_2$, in this order, so it is $1,2,1,3,1,2,1$.

Given $N$, print the entire sequence $S_N$.

Constraints

• $N$ is an integer.
• $1 \leq N \leq 16$

Input

Input is given from Standard Input in the following format:

$N$

Output

Print $S_N$, with spaces in between.

2

1 2 1

As described in the Problem Statement, $S_2$ is $1,2,1$.

1

1

4

1 2 1 3 1 2 1 4 1 2 1 3 1 2 1

• $S_4$ is a concatenation of $S_3$, $4$, and $S_3$, in this order.