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: Accepted)

#include <bits/stdc++.h>
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)
#define rep(i,n) FOR(i,0,n)
#define repr(i,n) for(int i=(n)-1;0<=i;--i)
#define dump(x) cerr<<#x<<": "<<x<<endl
#define debug(x) cerr<<#x<<": "<<x<<" ("<<__LINE__<<")"<<endl
using namespace std;
using vint = vector<int>;
using vdouble = vector<double>;
using vstring = vector<string>;
using ll = long long;
using vll = vector<ll>;
using P = pair<int, int>;

int main() {
    int n; cin >> n;
    vint p(n);
    rep(i, n) cin >> p[i];
    vint a(n), b(n);
    rep(i, n) {
        a[i] = n * i + 1;
        b[n-i-1] = n * i + 1;
    }
    rep(i, n) {
        b[p[i]-1] += i;
    }
    rep(i, n-1) cout << a[i] << " ";
    cout << a.back() << endl;
    rep(i, n-1) cout << b[i] << " ";
    cout << b.back() << endl;
    return 0;
}