Problem: 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.

Examples

Input

2
1 2


Output

1 4
5 4


Input

3
3 2 1


Output

1 2 3
5 3 1


Input

3
2 3 1


Output

5 10 100
100 10 1

Solution (in JAVA):

Solution:
import java.io.*;

public class Main {

	public static void main(String[] args) throws IOException {
		BufferedReader r = new BufferedReader(new InputStreamReader(System.in));
		int N = Integer.parseInt(r.readLine());
		String[] ps = r.readLine().split("\\s");
		int[] p = new int[N];
		for (int j = 0; j < N; j++)
			p[j] = Integer.parseInt(ps[j]);
		PrintWriter pw = new PrintWriter(System.out);
		for (int j = 0; j < N; j++) {
			pw.print(1 + (N + 1) * j);
			if (j < N-1)
				pw.print(" ");
		}
		pw.println();
		int[] b = new int[N];
		for (int j = 0; j < N; j++) {
			int il = (N + 1) * (N - p[j] + 1);
			b[p[j] - 1] = il + j - 1;
		}
		for (int j = 0; j < N; j++) {
			pw.print(b[j]);
			if (j < N-1)
				pw.print(" ");
		}
		pw.println();
		pw.close();
		r.close();
	}
	
}