Problem:
Score : 400 points

Problem Statement

#nck {
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}

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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>

int ip[20000], a[20000], b[20000];

int main(void){
    int i, N, p;
    
    scanf("%d", &N);
    
    for(i = 0; i < N ; i++){
        scanf("%d", &p);
        ip[p - 1] = i;
    }
    
    for(i = 0; i < N; i++) printf("%ld\n", ip[i]);
    
    for(i = 0; i < N; i++){
        a[i] = b[N - i - 1] = 20000 * i + 1;
    }
    
    for(i = 0; i < N; i++) a[i] += ip[i];
    
    
    printf("%ld", a[0]);
    for(i = 1; i < N; i++) printf(" %ld", a[i]);
    printf("\n%ld", b[0]);
    for(i = 1; i < N; i++) printf(" %ld", b[i]);
    printf("\n");

    return 0;
}