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 = list(map(int, input().split()))

A = [0 for _ in range(N)]
B = [0 for _ in range(N)]
X = [0 for _ in range(N)]
S = N
A[0] = 1
for i in range(N - 1):
  S += abs(p[i] - p[i-1])
for i in range(N):
  X[p[i]-1] = S + i
B[0] = X[0] - 1
for i in range(1, N):
  s = max(A[i-1] + 1, X[i] - B[i-1] + 1)
  A[i] = s
  B[i] = X[i] - s
if min(min(A), min(B)) <= 0:
  m = -min(min(A), min(B)) + 1
  for i in range(N):
    A[i] += m
    B[i] += m
for i in range(N):
  if i != N - 1:
    print(A[i], end = ' ')
  else:
    print(A[i])
for i in range(N):
  if i != N - 1:
    print(B[i], end = ' ')
  else:
    print(B[i])