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=tuple(map(int,input().split()))
if n==1:
    print(a[0])
else:
    b=tuple(sorted(a))
    A=list(itertools.permutations(b))
    count=len(A)-1

    if A.index(a)==count:
        print(' '.join(map(str,A[count-1])))
        print(' '.join(map(str,a)))
    elif A.index(a)==0:
        print(' '.join(map(str,b)))
        print(' '.join(map(str,A[1])))
    else:
        print(' '.join(map(str,A[A.index(a)-1])))
        print(' '.join(map(str,a)))
        print(' '.join(map(str,A[A.index(a)+1])))