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.*;
import java.util.*;
import java.util.Map.Entry;
import java.util.stream.Collectors;

@SuppressWarnings("unused")
public class Main {
	String fileName = "input.txt";
	final boolean isDebug = false;
	//final boolean isDebug = true;
	FastScanner in = new FastScanner(System.in);
	PrintWriter out = new PrintWriter(System.out);
	final int MOD = (int)1e9+7;
	final long INF = Long.MAX_VALUE / 2;
	//final int INF = Integer.MAX_VALUE / 2;
	
	void solve() throws Exception{
		//System.out.println();はつかわない！！
		int N = in.nextInt();
		int[] p = new int[N];
		int[] a = new int[N], b = new int[N];
		for(int i = 0; i < N; i++){
			p[i] = in.nextInt();
			a[i] = 1 + N * i;
			b[i] = (int)1e9 - N * i;
		}
		for(int i = 0; i < N; i++){
			a[p[i]-1] += i;
		}
		for(int i = 0; i < N; i++){
			out.print(a[i]);
			out.print(i == N-1 ? "\n" : " ");
		}
		for(int i = 0; i < N; i++){
			out.print(b[i]);
			out.print(i == N-1 ? "\n" : " ");
		}
	}
	
	/* end solve */
	
	/* main */
	public static void main(String[] args) throws Exception {
		new Main().m();
	}
	
	void m() throws Exception {
		if(isDebug) in = new FastScanner(new FileInputStream(fileName));
		solve();
		out.flush();
	}
	/* end main */
}
/* end Main */

class FastScanner {
	Reader input;

	FastScanner() {this(System.in);}
	FastScanner(InputStream stream) {this.input = new BufferedReader(new InputStreamReader(stream));}
	
	int nextInt() {return (int) nextLong();}

	long nextLong() {
		try {
			int sign = 1;
			int b = input.read();
			while ((b < '0' || '9' < b) && b != '-' && b != '+') {
				b = input.read();
			}
			if (b == '-') {
				sign = -1;
				b = input.read();
			} else if (b == '+') {
				b = input.read();
			}
			long ret = b - '0';
			while (true) {
				b = input.read();
				if (b < '0' || '9' < b) return ret * sign;
				ret *= 10;
				ret += b - '0';
			}
		} catch (IOException e) {
			e.printStackTrace();
			return -1;
		}
	}

	double nextDouble() {
		try {
			double sign = 1;
			int b = input.read();
			while ((b < '0' || '9' < b) && b != '-' && b != '+') {
				b = input.read();
			}
			if (b == '-') {
				sign = -1;
				b = input.read();
			} else if (b == '+') {
				b = input.read();
			}
			double ret = b - '0';
			while (true) {
				b = input.read();
				if (b < '0' || '9' < b) break;
				ret *= 10;
				ret += b - '0';
			}
			if (b != '.') return sign * ret;
			double div = 1;
			b = input.read();
			while ('0' <= b && b <= '9') {
				ret *= 10;
				ret += b - '0';
				div *= 10;
				b = input.read();
			}
			return sign * ret / div;
		} catch (IOException e) {
			e.printStackTrace();
			return Double.NaN;
		}
	}

	char nextChar() {
		try {
			int b = input.read();
			while (Character.isWhitespace(b)) {
				b = input.read();
			}
			return (char) b;
		} catch (IOException e) {
			e.printStackTrace();
			return 0;
		}
	}

	String nextStr() {
		try {
			StringBuilder sb = new StringBuilder();
			int b = input.read();
			while (Character.isWhitespace(b)) {
				b = input.read();
			}
			while (b != -1 && !Character.isWhitespace(b)) {
				sb.append((char) b);
				b = input.read();
			}
			return sb.toString();
		} catch (IOException e) {
			e.printStackTrace();
			return "";
		}
	}
}