Contest Duration: - (local time) (110 minutes) Back to Home
B - Construct Sequences /

Time Limit: 2 sec / Memory Limit: 256 MB

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.

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


問題文

• すべての i に対し、1 \leq a_i, b_i \leq 10^9
• 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}

制約

• 2 \leq N \leq 20,000
• p は集合 {1, 2, ..., N} の要素を並び替えた順列である。

入力

N
p_1 p_2 ... p_N


Output

2 行出力せよ。1 行目に整数列 a_1, a_2, ..., a_N を、2 行目に整数列 b_1, b_2, ..., b_N を、それぞれ空白区切りで出力せよ。

なお、制約を満たす任意の入力に対して解が存在することが示せる。

入力例 1

2
1 2


出力例 1

1 4
5 4


a_1 + b_1 = 6 および a_2 + b_2 = 8 より、すべての条件が満たされています。

入力例 2

3
3 2 1


出力例 2

1 2 3
5 3 1


入力例 3

3
2 3 1


出力例 3

5 10 100
100 10 1