Problem:
Score : 400 points

Problem Statement

#nck {
width: 30px;
height: auto;
}

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.

Sample Input 1

2
1 2

Sample Output 1

1 4
5 4

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

Sample Input 2

3
3 2 1

Sample Output 2

1 2 3
5 3 1

Sample Input 3

3
2 3 1

Sample Output 3

5 10 100
100 10 1

Solution in PHP (5.6.30) (judge verdict: Accepted)

<?php
class main {
    function run() {
        fscanf(STDIN, "%d", $n);
        $line = trim(fgets(STDIN));
        $p_arr = explode(" ", $line);

        $d = $n + 1;

        $a_arr = array();
        $b_arr = array();
        $r_arr = array();

        foreach ($p_arr as $k => $v) {
            $r_arr[$v] = $k;
        }

        for ($i = 1; $i <= $n; $i++) {
            $a_arr[] = $i * $d;
            $b_arr[] = ($n - $i) * $d + $r_arr[$i] + 1;
        }

        echo implode(" ", $a_arr) . "\n";
        echo implode(" ", $b_arr);
    }
}

$object = new main();
$object->run();