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<bits/stdc++.h>

using namespace std;

int main()
{
    long long n;
    cin>>n;
    vector<long long> a(n);
    for(long long i=0;i<n;i++)
    {
        cin>>a[i];
    }
    if(!is_sorted(a.begin(),a.end()))
    {
        prev_permutation(a.begin(),a.end());
        for(long long i=0;i<n;i++)
        {
            if(i)
                cout<<" ";
            cout<<a[i];
        }
        cout<<endl;
        next_permutation(a.begin(),a.end());
    }
    for(long long i=0;i<n;i++)
    {
        if(i)
            cout<<" ";
        cout<<a[i];
    }
    cout<<endl;
    if(next_permutation(a.begin(),a.end()))
    {
        for(long long i=0;i<n;i++)
        {
            if(i)
                cout<<" ";
            cout<<a[i];
        }
        cout<<endl;
        prev_permutation(a.begin(),a.end());
    }
    return 0;
}