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) for x in input().split()]

b = [None] * (n + 1)
b[P[0]] = 1
bs = {1}

for p, pprev in zip(P[1:], P):
    bp = b[pprev] + (pprev - p) * 20000 + 1
    while bp in bs:
        bp += 1
    b[p] = bp
    bs.add(bp)

offset = 1 - min(b[1:])
b = [i + offset for i in b[1:]]

print(' '.join([str(20000 * i) for i in range(1, n + 1)]))
print(' '.join([str(i) for i in b]))