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;
void print_v(vector<int> v)
{
    for (auto it = v.begin(); it != v.end() - 1; it++)
    {
        cout << *it << ' ';
    }
    cout << v.back() << endl;
}
int main()
{
    int n;
    cin >> n;
    vector<int> v;
    v.reserve(n);

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

    vector<int> prev, next;
    prev = v;
    next = v;

    if (prev_permutation(prev.begin(), prev.end()))
    {
        print_v(prev);
        print_v(v);
        if (next_permutation(next.begin(), next.end()))
        {
            print_v(next);
        }
    }
    else
    {
        print_v(v);
        if (next_permutation(next.begin(), next.end()))
        {
            print_v(next);
        }
    }
}