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(x) - 1 for x in input().split()]
A = [0] * N
B = [0] * N
D = [0] * N
for i, p in enumerate(P):
  D[p] = i
for i in range(P[0] + 1, N):
  if D[i] > D[i - 1]:
    B[i] = B[i - 1] - 1
    A[i] = D[i] - B[i]
  else:
    A[i] = A[i - 1] + 1
    B[i] = D[i] - A[i]
for i in range(P[0] - 1, -1, -1):
  if D[i] > D[i + 1]:
    A[i] = A[i + 1] - 1
    B[i] = D[i] - A[i]
  else:
    B[i] = B[i + 1] + 1
    A[i] = D[i] - B[i]
_a = 1 - A[0]
_b = 1 - B[-1]
print(' '.join([str(a + _a) for a in A]))
print(' '.join([str(b + _b) for b in B]))