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 CPP):

Solution:
#include "iostream"

using namespace std;

int N;
int num[20000];
int a[20000];
int b[20000];

int main() {
	cin >> N;
	for (int i = 0; i < N; i++) {
		cin >> num[i];
		a[i] = (i + 1)*N;
		b[i] += 2 * N*N - a[i];
		b[num[i]-1] += i+1;
	}
	for (int i = 0; i < N; i++)cout << a[i]<<" ";
	cout << "\n";
	for (int i = 0; i < N; i++)cout << b[i]<<" ";
	cout << "\n";
	return 0;
}