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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<cstdio>
int a,b,c,d,i,j,k;
int req[20005],up[20005],down[20005],target[20005];
int main(){
	scanf("%d",&a);
	for (i=1;i<=a;i++) {
		scanf("%d",&c);
		req[c]=i;
	}
	for (i=1;i<=a;i++) target[i]=500-a+req[i];
	up[1]=1;
	down[1]=target[1]-up[1];
	for (i=2;i<=a;i++){
		down[i]=down[i-1]-1;
		up[i]=target[i]-down[i];
		if (up[i]<=up[i-1]){
			c=up[i-1]-up[i]+1;
			up[i]+=c;
			down[i]-=c;
		}
	}
	for (i=1;i<=a-1;i++)  printf("%d ",up[i]);
	printf("%d\n",up[a]);
	for (i=1;i<=a-1;i++)  printf("%d ",down[i]);
	printf("%d\n",down[a]);
}