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: Wrong Answer)

#include <bits/stdc++.h>
#define ALL(a) (a).begin(), (a).end()
#define FOR(x,n) for(int x = 0; x < n; x++)
#define FORR(x,n) for(int x = n-1; x >= 0; x--)
#define FIN ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a) ((int)(a).size())
using namespace std;
typedef long long ll;

const int MXN = 20001;
int N, P[MXN];
int A[MXN], B[MXN];

int main(){
  cin >> N;
  int tmp1 = 4 * N, tmp2 = 4 * N * N;
  FOR(x,N) cin >> P[x], P[x]--, A[x] += tmp1, B[x] = tmp2, tmp1 += 4*N, tmp2 -= 4*N;
  FOR(x,N) {
    A[P[x]] -= (N-x);
    B[P[x]] -= (N-x);
  }
  
  FOR(x,N)
    cout << A[x] << " \n"[x+1==N];
  FOR(x,N)
    cout << B[x] << " \n"[x+1==N];
}