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:
n = int(input())
list = input().split()
for i in range(0,n):
   if int(list[i]) == n:
      p = i
      break

list1 = []
list2 = []
for k in range(0,n):
   list1.append(n* int ( list[k] ) - n + 1)
for k in range(0,n):
   list2.append( max ( int(list1[p] ) + 1 - p + k - int( list1[k] ), n - int ( list[k] ) +1))

a = ""
b = ""

list2.sort(reverse = True)
list1.sort()
for l in range (0,n):
   a += str(list1[l])
   a += " "
   b += str(list2[l])
   b += " "

print(a)
print(b)