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())
a = input()
b = range(1,n+1)

prev = ""
ans1 = ""
ans2 = ""
flag = False
for x in itertools.permutations(b):
	y = " ".join(list(map(str, x)))
	if flag:
		ans2 = y
		break
	if a==y:
		ans1 = prev
		flag = True
	prev = y
	
if ans1 != "":
	print(ans1)
print(a)
if ans2 != "":
	print(ans2)