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<algorithm>
#include<vector>

using namespace std;
vector<int>v;
void print()
{
    int ans=0;
    for(auto it=v.begin();it!=v.end();it++)
    {
        if(ans!=0)cout<<" ";
        cout<<*it;
        ans++;
    }
    cout<<endl;
}
int main()
{
    int n;
    cin>>n;
    v.resize(n);
    int i,j,k;
    for(i=0;i<n;i++)
    {
        cin>>v[i];
    }

    if(prev_permutation(v.begin(),v.end())==0)
    {
        //cout<<endl;
        next_permutation(v.begin(),v.end());
        print();
    if(next_permutation(v.begin(),v.end())==0)
    {
        //cout<<endl;
    }
    else {
    print();
    }
    }

    else
    {
        print();
        next_permutation(v.begin(),v.end());
        print();
        if(next_permutation(v.begin(),v.end())==0)
        {

        }
        else
        {
            print();
        }
    }

    return 0;
}