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:
#解説参照
#ap+bp=aq+bq作って微調整

n = int(input())
p = list(map(int, input().split( )))
for i in range(n):
    p[i]-=1
#n = 20
a = [5*10**8+i*20001 for i in range(n)]
b = [5*10**8-i*20001 for i in range(n)]
#import numpy as np
#p = np.random.permutation(n)
#print(*a)
for i in range(n):##2万差までひっくり返る
    a[p[i]] += i ##p[i],iに注意
   
print(*a)
print(*b)
"""
for i in range(n-1):
    assert a[i]<a[i+1],(a[i],a[i+1])
    assert b[i]>b[i+1],(b[i],b[i+1])
    assert a[p[i]]+b[p[i]]<a[p[i+1]]+b[p[i+1]],(i,p[i],a[p[i]],b[p[i]],a[p[i+1]],b[p[i+1]])
"""