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 <bits/stdc++.h>
using namespace std;
const int MAX = (2e4)+1;

int n, p[MAX], b[MAX];
int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	cin >> n;
	for(int i = 1; i <= n; i++) cin >> p[i];
	b[p[1]] = n*n;
	for(int i = 2; i <= n; i++) b[p[i]] = b[p[i-1]]-n*(p[i]-p[i-1])+1;
	for(int i = 1; i <= n; i++) cout << n*i << ' ';
	cout << endl;
	for(int i = 1; i <= n; i++) cout << b[i] << ' ';
}