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 CPP):

Solution:
#include <iostream>
#include <iterator>
#include <vector>
#include <algorithm>
#include <string>

using namespace std;


void output(vector<int> & V);

int main()
{
    vector<int> V;

    int n;
    cin >> n;

    int a;
    while (n--)
    {
        cin >> a;
        V.push_back(a);
    }

    if (prev_permutation(V.begin(), V.end()))
        output(V);
    
    next_permutation(V.begin(), V.end());
    output(V);

    if (next_permutation(V.begin(), V.end()))
        output(V);


}


void output(vector<int> & V)
{
    vector<int>::iterator it = V.begin();
    cout << *it++;
    while (it != V.end())
    {
        
        cout << ' ' << *it;
        it++;
    }
    cout << endl;
}