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:
import sys
input = sys.stdin.readline
N = int(input())
p = list(map(int, input().split()))
res = [0] * N
for i in range(N):
  res[p[i] - 1] = 10 ** 9 - N + i + 1

a = [1]
b = [res[0] - 1]
for i in range(1, N):
  if res[i] - a[-1] - 1 >= b[-1]:
    b.append(b[-1] - 1)
    a.append(res[i] - b[-1])
  else:
    a.append(a[-1] + 1)
    b.append(res[i] - a[-1])
print(*a)
print(*b)