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:
import itertools

n = int(input())
num = list(map(int, input().split()))
per = list(itertools.permutations(num))

per.sort()
index = per.index(tuple(num))

if index != 0:
    print(' '.join(str(n) for n in per[index-1]))
print(' '.join(str(n) for n in per[index]))
if index != len(per)-1:
    print(' '.join(str(n) for n in per[index+1]))