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:
def main():
    N = int( input())
    Q = list( map( int, input().split()))
    P = [0]*N
    for i in range(N):
        P[Q[i]-1] = i+1
    A = [1]
    B = [1]
    for i in range(N-1):
        if P[i] < P[i+1]:
            A.append(A[-1] + P[i+1] - P[i] + 1)
        else:
            A.append(A[-1] + 1)
    for i in range(N-2,-1,-1):
        if P[i] > P[i+1]:
            B.append(B[-1] + P[i] - P[i+1] + 1)
        else:
            B.append(B[-1]+1)
    print(" ".join( map(str, A)))
    print(" ".join( map(str, B[::-1])))
if __name__ == '__main__':
    main()