Problem Statement

You are given a positive integer $N$.

There is a complete binary tree with $2^N-1$ vertices. The vertices are numbered $1$ through $2^N-1$.

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

Find one way to write an integer between $1$ and $2^N-1$, inclusive, on the vertices (where all $2^N-1$ written integers are distinct) such that the following condition is satisfied.

• For each $i\ (1\leq i\lt 2^{N-1})$, 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 $2i+1$ is $1$.

It can be proved that there always exists a way to write the integers satisfying the condition under the constraints of this problem.

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 $i$. Output:

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

$(P_1,P_2,\ldots,P_{2^N-1})$ must be a permutation of $(1,2,\ldots,2^N-1)$.

If there are multiple valid ways to write the integers, any of them will be accepted.