Problem: For given a sequence $A = \\{a_0, a_1, ..., a_{n-1}\\}$, print the previous permutation and the next permutation in lexicographic order.

Constraints

* $1 \leq n \leq 9$
* $a_i$ consist of $1, 2, ..., n$

Input

A sequence is given in the following format.


$n$
$a_0 \; a_1 \; ... \; a_{n-1}$


Output

Print the previous permutation, the given sequence and the next permutation in the 1st, 2nd and 3rd lines respectively. Separate adjacency elements by a space character. Note that if there is no permutation, print nothing in the corresponding line.

Examples

Input

3
2 1 3


Output

1 3 2
2 1 3
2 3 1


Input

3
3 2 1


Output

3 1 2
3 2 1

Solution (in PYTHON3):

Solution:
from itertools import permutations



# INPUT
n = int(input())

A = tuple(input().split())


# PROCESS, OUTPUT
str_num = ""

for num in range(1, n + 1):
    str_num += str(num)


flag_break = False
list_num_previous = None

for list_num in permutations(str_num):
    if flag_break:
        # next
        print(*list_num)
        break

    if list_num == A:
        if list_num_previous != None:
            # previous
            print(*list_num_previous)

        # now
        print(*list_num)
        flag_break = True

    list_num_previous = list_num