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:
n = int(input())
p = [int(i) for i in raw_input().split()]
a = [0 for i in range(n)]
b = [0 for i in range(n)]
p.reverse()
for i in range(n):
	k = p.pop()
	a[k-1] = i + 1
	b[k-1] = i + 1
for i in range(1,n):
	d = min(a[i] - a[i-1],b[i-1] - b[i])
	if d <= 0:
		a[i] -= d - 1
		b[i] += d - 1
ma = min(a)
mb = min(b)
a = [str(i+1-ma) for i in a] 
b = [str(i+1-mb) for i in b]
print(" ".join(a))
print(" ".join(b))