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:
from operator import itemgetter
N = int(input())
P = list(map(int, input().split()))

# とりあえずBを決定しておいて、Aを良い感じに決める
# BはN間隔にすると良い感じになる
A = [-1] * N
B = [N * i for i in range(1, N + 1)][::-1]

for i, p in enumerate(P):
    p -= 1
    if i == 0:
        A[p] = (p + 1) * N
        AB = A[p] + B[p]
        continue
    A[p] = AB - B[p] + 1
    AB = A[p] + B[p]

print(*A)
print(*B)