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:
# -*- coding: utf-8 -*-
"""
Permutation - Permutation
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP2_5_C&lang=jp

"""
from itertools import permutations

n = int(input())
A = tuple(map(int, input().split()))
res = [p for p in permutations(sorted(A), n)]
i = res.index(A)
for a in res[max(0, i-1):i+2]:
    print(*a)