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: Accepted)

N = gets.to_i
ps = gets.split.map(&:to_i)
#N = 20000
#ps = (1..20000).to_a.shuffle
rev = []
N.times do |i|
    rev[ps[i]-1] = i
end

as, bs = [1], [10**9]
(N-1).times do |i|
    diff = rev[i+1] - rev[i]
    if diff > 0
        as[i+1] = as[i] + diff + 1
        bs[i+1] = bs[i] - 1
    else
        as[i+1] = as[i] + 1
        bs[i+1] = bs[i] + diff - 1
    end
end
puts as.join(' ')
puts bs.join(' ')

#(N-1).times do |i|
#    if as[ps[i]-1] + bs[ps[i]-1] >= as[ps[i+1]-1] + bs[ps[i+1]-1]
#        puts 'WA'
#        exit
#    end
#end