Problem:
Score : 400 points

Problem Statement

#nck {
width: 30px;
height: auto;
}

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.

Sample Input 1

2
1 2

Sample Output 1

1 4
5 4

a_1 + b_1 = 6 and a_2 + b_2 = 8. So this output satisfies all conditions.

Sample Input 2

3
3 2 1

Sample Output 2

1 2 3
5 3 1

Sample Input 3

3
2 3 1

Sample Output 3

5 10 100
100 10 1

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pii;

#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define N 100000
#define MOD 1000000007
#define INF 1000000000

int main()
{
        int n;
        int p[20000] = {};
        cin >> n;
        for(int i = 0; i < n; i++){
                cin >> p[i];
                p[i]--;
        }
        int a[20000] = {};
        int b[20000] = {};
        int sum[20000] = {};
        int cnt = 0;
        for(int i = 0; i < n; i++){
                sum[ p[i] ] = i;
        }

        for(int i = 0; i < n; i++){
                int curSum = 500000000 + sum[i];
                if(i == 0){
                        a[i] = 1;
                        b[i] = curSum - 1;
                }
                else{
                        int prev = a[i - 1];
                        a[i] = a[i - 1] + 1;
                        b[i] = curSum - a[i];
                        while(b[i] >= b[i - 1]){
                                b[i]--;
                                a[i]++;
                        }
                }
        }

        for(int i = 0; i < n; i++){
                cout << a[i] << ' ';
        }
        cout << endl;
        for(int i = 0; i < n; i++){
                cout << b[i] << ' ';
        }


        return 0;
}