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
from collections import deque
import copy
import math
def get_read_func(fileobject):
    if fileobject == None :
        return raw_input
    else:
        return fileobject.readline


def main():
    if len(sys.argv) > 1:
        f = open(sys.argv[1])
    else:
        f = None
    read_func = get_read_func(f);
    input_raw = read_func().strip().split()
    [N] = [int(input_raw[0])]
    input_raw = read_func().strip().split()
    P = [int(input_raw[i]) for i in range(N)]
    P_inv = {}

    A = {}
    B = {}
    A[P[0]] = P[0] * N + 1
    B[P[0]] = P[0] * N + 1
    min_B = B[P[0]]
    min_A = A[P[0]]
    for i in range(1, N):

        if P[i] > P[i - 1]:
            A[P[i]] = A[P[i - 1]]  + N*(P[i] - P[i - 1])
            B[P[i]] = B[P[i - 1]] - N *(P[i] - P[i - 1])
        else:
            A[P[i]] = A[P[i - 1]]  - N *(P[i - 1] - P[i])
            B[P[i]] = B[P[i - 1]] + N *(P[i - 1] - P[i])
        min_A = min(min_A, A[P[i]])
        min_B = min(min_B, B[P[i]])

    for i in range(1, N + 1):
        A[P[i - 1]] += -min_A + 1
        B[P[i - 1]] += -min_B + 1
    for i in range(1, N + 1):
        A[P[i - 1]] += i
    for i in range(1, N + 1):
        print A[i],
    print
    for i in range(1, N + 1):
        print B[i],





if __name__ == '__main__':
    main()