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.*;

class Main {
        public static void main(String args[]) {
                try (Scanner sc = new Scanner(System.in)) {
                        int N = sc.nextInt();
                        long[] A = new long[N];
                        long[] B = new long[N];
                        for (int i = 0; i < N; i++) {
                                A[i] = i * 10001L + 1;
                                B[N-i-1] = i * 10001L + 1;
                        }
                        for (int i = 0; i < N; i++) {
                                int p = sc.nextInt();
                                p--;
                                A[p] += i / 2;
                                B[p] += i - i / 2;
                        }
                        for (int i = 0; i < N; i++) {
                                System.out.print(A[i]);
                                if (i == N - 1) {
                                        System.out.print("\n");
                                } else {
                                        System.out.print(" ");
                                }
                        }
                        for (int i = 0; i < N; i++) {
                                System.out.print(B[i]);
                                if (i == N - 1) {
                                        System.out.print("\n");
                                } else {
                                        System.out.print(" ");
                                }
                        }
                }
        }
}