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:
#import string,itertools,fractions,heapq,re,array,bisect
#from math import *
#from collections import Counter
def rl(s): return xrange(len(s))

INF = 2147483647


import sys
stdin = sys.stdin

N =        int( stdin.readline().strip() )
ps = map(int, stdin.readline().strip().split())

heights = [0] * N
for i, p in enumerate(ps):
    heights[p-1] = i

aa = [1 + 21000*i for i in range(N)]
bb = [heights[i] - aa[i] for i in range(N)]
base = min(bb)
bb = [b + abs(base)+1 for b in bb]

print ' '.join(map(str, aa))
print ' '.join(map(str, bb))