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 sys

def rl(proc=None):
    if proc is not None:
        return proc(sys.stdin.readline())
    else:
        return sys.stdin.readline().rstrip()

def srl(proc=None):
    if proc is not None:
        return map(proc, rl().split())
    else:
        return rl().split()

def fix(a):
    mn = min(a) - 1
    return [x - mn for x in a]

def main():
    N = rl(int)
    p = srl(int)
    a = range(N)
    b = list(reversed(a))
    inc = [0] * (N+1)
    for i, v in enumerate(p[1:], 1):
        a[v-1] += i
        inc[v] += i
    s = 0
    for i in xrange(N):
        s += inc[i]
        a[i] += s
        b[i] -= s
    print " ".join(map(str, fix(a)))
    print " ".join(map(str, fix(b)))

if __name__ == '__main__':
    main()