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<vector>
#include<algorithm>
using namespace std;

void print( vector<int> v )
{
    int n = v.size();
    for( int i = 0; i < n - 1; i++ )
    {
        cout << v[i] << " ";
    }
    cout << v[n-1] << endl;
}

int main()
{
    int n, m;
    vector<int> v;

    cin >> n;

    for( int i = 0; i < n; i++ )
    {
        cin >> m;
        v.push_back(m);
    }

    if( prev_permutation( v.begin(), v.end() ) == true )
        print(v);
    else
    {
        next_permutation( v.begin(), v.end() );
        print(v);
        if( next_permutation( v.begin(), v.end() ) == true )
            print(v);
        return 0;
    }

    if( next_permutation( v.begin(), v.end() ) == true )
        print(v);

    if( next_permutation( v.begin(), v.end() ) == true )
        print(v);

    return 0;
}