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.BufferedReader;
import java.io.InputStreamReader;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] sa = br.readLine().split(" ");
		int n = Integer.parseInt(sa[0]);

		sa = br.readLine().split(" ");
		int[] p = new int[n];
		for (int i = 0; i < n; i++) {
			p[i] = Integer.parseInt(sa[i]) - 1;
		}
		br.close();

		int[] d = new int[n];
		for (int i = 0; i < n; i++) {
			d[p[i]] = i;
		}

		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < n; i++) {
			sb.append(20000 * (i + 1) + d[i]).append(' ');
		}
		sb.deleteCharAt(sb.length() - 1);
		System.out.println(sb.toString());

		sb = new StringBuilder();
		for (int i = 0; i < n; i++) {
			sb.append(400000000 - 20000 * i).append(' ');
		}
		sb.deleteCharAt(sb.length() - 1);
		System.out.println(sb.toString());
	}
}