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 = list(map(int, input().split()))
P = [p-1 for p in P]

A=  list(range(1, n+1))
B = list(reversed(range(1, n+1)))

C = [0]*(n+1)
D = [0]*(n+1)
for i in range(n):
    p = P[i]
    C[p] += i+1
    C[n] -= i+1
    D[0] += i+1
    D[p+1] -= i+1
from itertools import accumulate
C = list(accumulate(C))
D = list(accumulate(D))

A_ = [0]*n
B_ = [0]*n
for i in range(n):
    A_[i] = A[i] + C[i]
    B_[i] = B[i] + D[i]

print(*A_)
print(*B_)