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 INCANT cin.tie(0), cout.tie(0), ios::sync_with_stdio(false), cout << fixed << setprecision(20);
#define int long long
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(), (x).end()
#define _overload(_1, _2, _3, name, ...) name
#define _rep(i, n) repi(i, 0, n)
#define repi(i, a, b) for(int i = (int)(a); i < (int)(b); i++)
#define rep(...) _overload(__VA_ARGS__, repi, _rep)(__VA_ARGS__)
#define _rev(i, n) revi(i, n, 0)
#define revi(i, a, b) for(int i = (int)(a - 1); i >= (int)(b); i--)
#define rev(...) _overload(__VA_ARGS__, revi, _rev)(__VA_ARGS__)
#define each(i, n) for(auto&& i: n)
void in(){}
template<typename F, typename... R>
bool in(F& f, R&... r){
    if(cin >> f){in(r...);return true;}
    else return false;
}
#define out(x) cout << (x)
#define space() cout << " "
#define indent() cout << '\n'
void print(){}
template<typename F, typename... R>
void print(F f, R... r){out(f), indent(), print(r...);}
#define debughead(x) cerr << "Line " << __LINE__ << ": " << #x << ": "
#define debugout(x) cerr << (x) << " "
#define debugindent() cerr << '\n'
#define debug(x) debughead(x), debugout(x), debugindent()
const int INF = 1e18, MOD = 1e9 + 7;
template<typename T>
bool chmax(T& a, T b){return (a = max(a, b)) == b;}
template<typename T>
bool chmin(T& a, T b){return (a = min(a, b)) == b;}

main(){
    INCANT;
    int n, p, tmp, tmp2, res = -INF;
    string s;
    in(n);
    int a[n], b[n], r[n];
    rep(i, n){
        in(p);
        r[p - 1] = i;
    }
    rep(i, n){
        a[i] = 30000 * i;
        b[i] = 30000 * n - a[i] + r[i];
    }
    rep(i, n){
        if(i){
            space();
        }
        out(a[i]);
    }
    indent();
    rep(i, n){
        if(i){
            space();
        }
        out(b[i]);
    }
}