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:
def rec(lst,d):
    for i in range(1,len(lst)+1):
        if i not in lst:
            lst[d]  = i
            if d+1 == len(lst):
                a = list(lst)
                P.append(a)
                lst[d] = 0
                return
            else:
                rec(lst,d+1)
                lst[d] = 0

N = int(input())
S = list(map(int,input().split()))

P = []

lst = []
for i in range(N):
    lst.append(0)

rec(lst,0)

for i in range(len(P)):
    if S == P[i]:
        if i != 0:
            print(*P[i-1])
        print(*P[i])
        if i+1 != len(P):
            print(*P[i+1])