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(i) for i in input().split()]
asum = [1] * (N + 1)
bsum = [-1] * (N + 1)
bsum[0] = N
for i in range(N):
    p = P[i] - 1
    asum[p + 1] += 20000 - i
    bsum[0] += 20000 - i
    bsum[p] -= 20000 - i
a = [0] * N
b = [0] * N
a[0] = asum[0]
b[0] = bsum[0]
for i in range(1, N):
    a[i] = a[i - 1] + asum[i]
    b[i] = b[i - 1] + bsum[i]
for i in range(N):
    print(a[i], end=' ')
print()
for i in range(N):
    print(b[i], end=' ')