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()))
A = [1 for _ in range(N+1)]
B = [0 for _ in range(N+1)]
L = [0 for _ in range(N+1)]
for i in range(N):
    L[P[i]] = 2*i
B[1] = L[1]-A[1]
for i in range(2,N+1):
    if L[i]>L[i-1]:
        B[i] = B[i-1]-1
        A[i] = L[i]-B[i]
    else:
        A[i] = A[i-1]+1
        B[i] = L[i]-A[i]
b = abs(B[-1])+1
for i in range(1,N+1):
    B[i] += b
print(*A[1:])
print(*B[1:])