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:
"""from collections import *
from itertools import *
from bisect import *
from heapq import *

import math
from fractions import gcd
import sys
#input = sys.stdin.readline

import copy
"""
N=int(input())
P=list(map(int,input().split()))
for i in range(N):
    P[i]-=1
A=[30000*i for i in range(1,N+1)]
B=list(reversed(A))
ruiA=[]
ruiB=[]


#lst=set(P[1:])
count=1
for i in range(0,N)[::-1]:
    B[P[i]]-=count
    """for m in lst:
        B[m]-=1
    lst.add(P[i])"""
    count+=1

print(" ".join([str(i) for i in A]))
print(" ".join([str(i) for i in B]))