Problem Statement

Given is an integer sequence $a$ of length $2N$.

Snuke is going to make a sequence using a non-empty (not necessarily contiguous) subsequence $x=(x_1,x_2,\ldots,x_k)$ of $(1,2, \ldots, N)$. The sequence will be made by extracting and concatenating the $x_1$-th, $x_2$-th, $\ldots$, $x_k$-th, $(x_{1}+N)$-th, $\ldots$, $(x_{k}+N)$-th elements of $a$ in this order.

Find the lexicographically smallest sequence that Snuke can make.

Lexicographical order on sequences Here is the algorithm to determine the lexicographical order between different sequences $S$ and $T$. Below, let $S_i$ denote the $i$-th element of $S$. Also, if $S$ is lexicographically smaller than $T$, we will denote that fact as $S \lt T$; if $S$ is lexicographically larger than $T$, we will denote that fact as $S \gt T$. Let $L$ be the smaller of the lengths of $S$ and $T$. For each $i=1,2,\dots,L$, we check whether $S_i$ and $T_i$ are the same. If there is an $i$ such that $S_i \neq T_i$, let $j$ be the smallest such $i$. Then, we compare $S_j$ and $T_j$. If $S_j$ is smaller than $T_j$ in numerical order, we determine that $S \lt T$ and quit; if $S_j$ is greater than $T_j$, we determine that $S \gt T$ and quit. If there is no $i$ such that $S_i \neq T_i$, we compare the lengths of $S$ and $T$. If $S$ is shorter than $T$, we determine that $S \lt T$ and quit; if $S$ is longer than $T$, we determine that $S \gt T$ and quit.

Constraints

• All values in input are integers.
• $1 \leq N \leq 10^5$
• $1 \leq a_i \leq 10^9$

Input

Input is given from Standard Input in the following format:

N
a_{1} \cdots a_{2N}

Output

Print the lexicographically smallest sequence that Snuke can make.