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.

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.

Constraints

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

Sample Input 1

3
2 1 3 1 2 2

Sample Output 1

1 2

• We choose x = (2).
• Then, the resulting sequence will be (1,2), the lexicographically smallest possible result.

Sample Input 2

10
38 38 80 62 62 67 38 78 74 52 53 77 59 83 74 63 80 61 68 55

Sample Output 2

38 38 38 52 53 77 80 55

Sample Input 3

12
52 73 49 63 55 74 35 68 22 22 74 50 71 60 52 62 65 54 70 59 65 54 60 52

Sample Output 3

22 22 50 65 54 52

见题面 Input 部分

见题面 Output 部分