Problem: 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.

Examples

Input

2
1 2


Output

1 4
5 4


Input

3
3 2 1


Output

1 2 3
5 3 1


Input

3
2 3 1


Output

5 10 100
100 10 1

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
#define rep(i,a,b) for(int i=int(a);i<int(b);++i)
using namespace std;
typedef long long ll;
int INF = (1LL << 30) - 1;
int MOD = 1e9+7;
int main(){
    int N;
    cin >> N;
    vector<int> V(N);
    rep(i,0,N)cin >> V[i];
    vector<int> A(N),B(N);
    rep(i,0,N)A[i] = B[N-i-1] = (i+1) * 30000;
    rep(i,0,N){
        B[V[i] - 1] += i;
    }
    rep(i,0,N)cout << A[i] << " \n"[i==N-1];
    rep(i,0,N)cout << B[i] << " \n"[i==N-1];
}