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
import copy
n = int(input())
l = list(map(int,input().split()))
l2 = copy.deepcopy(l)
l.sort()
ans = []
for i in itertools.permutations(l,n):
    ans.append(list(i))

for i in range(len(ans)):
    if ans[i] == l2:
        if i - 1 >= 0:
            print(' '.join(map(str,(ans[i - 1]))))
        print(' '.join(map(str,(ans[i]))))
        if i != len(ans) - 1:
            print(' '.join(map(str,(ans[i + 1]))))
        break