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:
#B問題
N = int(input())
P = list(map(int,input().split()))
A = []
B = []
for i in range(N):
    P[i]-=1
    A.append(40000*(i+1))
    B.append(40000*(N-i))
    
add = 0
C = []
for p in P:
    if len(C) == 0:
        C.append(A[p]+B[p])
    else:
        c = C[-1]
        if c < A[p]+B[p]+add:
            C.append(A[p]+B[p]+add)
        else:
            add+=c-(A[p]+B[p]+add)+1
            C.append(A[p]+B[p]+add)
    A[p]+=add
    
for a in A:
    print(a+add,end=" ")
print()
for b in B:
    print(b,end=" ")