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 PYTHON3):

Solution:
N=int(input())
p=[(int(a),i+1) for i,a in enumerate(input().split())]
p.sort()
a=[0]*N
b=[0]*N
a[0]=p[0][1]
b[0]=10**9
for i in range(1,N):
  if p[i][1]>p[i-1][1]:
    a[i]=a[i-1]+p[i][1]-p[i-1][1]+1
    b[i]=b[i-1]-1
  if p[i][1]<p[i-1][1]:
    a[i]=a[i-1]+1
    b[i]=b[i-1]+p[i][1]-p[i-1][1]-1
    
print(" ".join(list(map(str,a))))
print(" ".join(list(map(str,b))))