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:
import sys
import heapq
import bisect

mod = 10**9+7
dd = ((-1,0),(1,0),(0,-1),(0,1))

def I(): return(int(sys.stdin.readline()))
def LI(): return([int(x) for x in sys.stdin.readline().split()])
def S(): return(sys.stdin.readline()[:-1])
def IR(n): return([I() for _ in range(n)])

def GCD(a,b):
    while b!=0:
        a,b = b,a%b
    return a

def LCM(a,b):
    return a * b // GCD(a,b)

def main():
    N = I()
    P = LI()

    a = [45000*i + 1 for i in range(N)]
    b = [45000*(N-1-i) + 1 for i in range(N)]

    for i in range(N):
        a[P[i]-1] += i
        b[P[i]-1] += i

    print(" ".join(map(str,a)))
    print(" ".join(map(str,b)))






if __name__ == "__main__":
    main()