Problem Statement

You are given a positive integer $N$.

There is a perfect binary tree with $2^N - 1$ vertices. The vertices are numbered from $1$ to $2^N - 1$.

Vertex $1$ is the root, and for each vertex $i$ ($1 \leq i < 2^{N - 1}$), vertex $i$ has vertex $2i$ and vertex $2i + 1$ as its children.

Among the ways to write an integer between $1$ and $2^N - 1$, inclusive, on each vertex (where the $2^N - 1$ written integers must be pairwise distinct) such that the following condition is satisfied, find one that minimizes the integer written on vertex $1$.

• For each vertex $i$ ($1 \leq i < 2^{N - 1}$), the integer written on vertex $i$ is the absolute difference between the sum of the integers written on the vertices of the subtree rooted at vertex $2i$ and the sum of the integers written on the vertices of the subtree rooted at vertex $2i+1$.

It can be proved that, under the constraints of this problem, a way of writing integers satisfying the condition always exists.

Constraints

• $2 \leq N \leq 18$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N

Output

Let $P_i$ be the integer written on vertex $i$ ($1 \leq i \leq 2^N - 1$), and output in the following format:

P_1 P_2 \cdots P_{2^N - 1}

$(P_1, P_2, \cdots, P_{2^N - 1})$ must be a permutation of $(1, 2, \cdots, 2^N - 1)$. If there are multiple ways of writing satisfying the condition that minimize the integer written on vertex $1$, any of them will be considered correct.