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(_) for _ in input().split()]
a = []
b = []
for i in range(1, n + 1):
    a.append(i * 2 * n)
    b.append((n + 1 - i) * 2 * n)
d = 1
for i in p:
    if d % 2 == 0:
        a[i - 1] += d // 2
        b[i - 1] += d // 2
    else:
        a[i - 1] += d // 2
        b[i - 1] += d // 2
        if a[i - 1] >= b[i - 1]:
            b[i - 1] += 1
        else:
            a[i - 1] += 1
    d += 1
for i in a:
    print(i, end=' ')
print()
for i in b:
    print(i, end=' ')