Score : $600$ points

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.

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.

3
2 1 3 1 2 2

1 2

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

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

38 38 38 52 53 77 80 55

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

22 22 50 65 54 52