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 random import shuffle
from collections import Counter
def inpl(): return list(map(int, input().split()))

#N = 20000
#P = list(range(1, N+1))
#shuffle(P)

N = int(input())
P = inpl()

A = [0]*N
B = [0]*N
S = [10**9 - N] * (N)
for i, p in enumerate(P):
    S[p-1] += i

A[0] = 1
B[0] = S[0] - 1

for i in range(1, N):
    A[i] = max(A[i-1] + 1, S[i] - B[i-1] + 1)
    B[i] = S[i] - A[i]

for i in range(N-1):
    assert A[i] < A[i+1]
    assert B[i] > B[i+1]

assert B[-1] > 0
print(*A)
print(*B)