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 Ruby (2.3.3) (judge verdict: Wrong Answer)


N = gets.to_i

index_list = []

gets.strip.split(/ /).each_with_index{|n, i|
	j = n.to_i - 1
	index_list[j] = i
}

last_a = 0
last_b = 0
a_list = []
b_list = []

index_list.each{|i|
	a = last_a + 1
	b = last_b - 1
	if a + b <= i
		cand_a = i - 1 - b
		cand_b = i - 1 - a
		if cand_a >= a
			a = cand_a
		elsif cand_b <= b
			b = cand_b
		else
			raise
		end
	end
	a_list << a
	b_list << b
	last_a = a
	last_b = b
}

b_base = 1 - b_list.min

puts a_list.join(" ")
puts b_list.collect{|n| n + b_base}.join(" ")