Score : $400$ points

Problem Statement

You are given a permutation $p$ of the set {$1, 2, ..., N$}. Please construct two sequences of positive integers $a_1$, $a_2$, ..., $a_N$ and $b_1$, $b_2$, ..., $b_N$ satisfying the following conditions:

• $1 \leq a_i, b_i \leq 10^9$ for all $i$
• $a_1 < a_2 < ... < a_N$
• $b_1 > b_2 > ... > b_N$
• $a_{p_1}+b_{p_1} < a_{p_2}+b_{p_2} < ... < a_{p_N}+b_{p_N}$

Constraints

• $2 \leq N \leq 20,000$
• $p$ is a permutation of the set {$1, 2, ..., N$}

Input

The input is given from Standard Input in the following format:

$N$

$p_1$ $p_2$ $...$ $p_N$

Output

The output consists of two lines. The first line contains $a_1$, $a_2$, ..., $a_N$ seperated by a space. The second line contains $b_1$, $b_2$, ..., $b_N$ seperated by a space.

It can be shown that there always exists a solution for any input satisfying the constraints.

2
1 2

1 4
5 4

$a_1 + b_1 = 6$ and $a_2 + b_2 = 8$. So this output satisfies all conditions.

3
3 2 1

1 2 3
5 3 1

3
2 3 1

5 10 100
100 10 1