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 PYTHON):

Solution:
N = input()
P = map(lambda x:int(x)-1, raw_input().split())

MAX = 10**9
A = [MAX/(N-1)*i for i in xrange(N)]
A[0] += 1
B = A[::-1]

t = 0
for p in P:
    if A[p] + B[p] > t:
        t = A[p] + B[p]
    elif p == N-1:
        B[p] += t+1-A[p]-B[p]
        t += 1
    else:
        A[p] += t+1-A[p]-B[p]
        t += 1
print ' '.join(map(str, A))
print ' '.join(map(str, B))