Problem Statement

An almost complete binary tree is a binary tree with $2^{K}-1$ vertices whose height is at least $K$ and at most $3K$. The height is the distance from the root to the farthest vertex, where each edge has length $1$.
Today, once again, you have decided to construct $1$ almost complete binary tree.

The construction procedure is determined by a sequence $P_1, P_2, \ldots, P_{2^K - 1} $ that is a permutation of $\{1, 2, 3 , \ldots, 2^{K} - 1 \}$.
Specifically, starting from a binary search tree $T$ consisting of $0$ elements, you insert $P_1, P_2, \ldots , P_{2^{K}- 1}$ in this order.
The rule for inserting a value $v$ into a binary search tree $G$ is defined recursively as follows.

• If $G$ has no vertices, make $v$ the root of $G$.
• If $G$ has vertices, compare $v$ with the value of the root. If $v$ is smaller, insert it into the left subtree; otherwise, insert it into the right subtree.

For example, when $K=2$, $( 1,3,2 ), (2,1,3)$ finally yield the binary trees shown in the figures below, respectively.
The binary tree obtained from $( 1,3,2 )$ has height $2$, so it is an almost complete binary tree, but the binary tree obtained from $(2,1,3 )$ has height $1$, so it is not an almost complete binary tree.

Find any $1$ sequence such that the binary search tree $T$ obtained by this procedure is an almost complete binary tree.
It is guaranteed that at least $1$ solution exists.

Input

$K$

An integer $K(2 \leq K \leq 12)$ is given in $1$ line.

Output

Output the sequence $P$ that determines the construction procedure of a binary tree satisfying the condition, separated by spaces, in $1$ line.
Any sequence satisfying the condition will be accepted.

Sample