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.util.Scanner;

public class Main {
    public static void main(String args[]) {
        try (Scanner in = new Scanner(System.in)) {
            int N = in.nextInt();
            int[] p = new int[N];
            for (int i = 0; i < N; i++) {
                p[i] = in.nextInt() - 1;
            }
            int[] a = new int[N];
            int[] b = new int[N];
            for (int i = 0; i < N; i++) {
                a[i] = 40000 * i;
                b[N - 1 - i] = 40000 * i;
            }
            for (int i = 0; i < N; i++) {
                a[p[i]] += i;
            }

//            int[] sum = new int[N];
//            for (int i = 0; i < N; i++) {
//                sum[i] = a[i] + b[i];
//            }
//            for (int i = 0; i < N; i++) {
//                if (i - 1 >= 0 && a[i - 1] >= a[i]) {
//                    Utils.debug("a[i - 1] >= a[i]");
//                }
//                if (i - 1 >= 0 && b[i - 1] <= b[i]) {
//                    Utils.debug("b[i - 1] <= b[i]");
//                }
//                if (i - 1 >= 0 && sum[p[i - 1]] >= sum[p[i]]) {
//                    Utils.debug("sum[p[i - 1]] >= sum[p[i]]");
//                }
//            }

            StringBuilder sb = new StringBuilder();
            for (int i = 0; i < N; i++) {
                if (i > 0) {
                    sb.append(" ");
                }
                sb.append(a[i] + 1);
            }
            sb.append("\n");
            for (int i = 0; i < N; i++) {
                if (i > 0) {
                    sb.append(" ");
                }
                sb.append(b[i] + 1);
            }
            System.out.println(sb.toString());
        }
    }
}