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>
using  namespace std;

#define endl '\n'
#define ll long long
#define re register
#define pb(x) push_back(x)
#define ce(x) cout << x << '\n';

using db = long double;
using pll = pair < ll, ll >;

#define rep(i,x,n,inc) for(i=x ; i<n ; i+=inc)
#define repr(i,x,n,inc) for( i=x ; i>n ; i+=inc)
#define all(a)      (a).begin(),(a).end()
#define unique_sort(x) sort(all(x)), x.resize(distance(x.begin(), unique(all(x))))

#define mp(a,b) make_pair(a,b)
#define ff first
#define ss second
#define hell 1000000007
const db pi = acos(-1);
const long long infl = LLONG_MAX;

#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
#define Fill(s,v) memset(s,v,sizeof(s))
#define cout_p(x, p) cout << fixed << setprecision((p)) << x << endl     //print with precision

#define tc(tt) \
    ll tt;    \
    cin >> tt; \
    for (ll _tt = 0; _tt < tt; _tt++) // testcase 

int32_t main(){
ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);


ll t,i,x,j,y,z,k,n;
cin>>n;
ll p[n+1],a[n+1],b[n+1];
rep(i,1,n+1,1){
	cin>>x;
	p[x]=i;
}

rep(i,1,n+1,1){
	a[i]=i;
	cout<<a[i]<<" ";
}
ce("")

rep(i,1,n+1,1){
	b[i]=n-i+p[i];
	cout<<b[i]<<" ";
}


}