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;

int main()
{
	int n;

	cin >> n;
	vector<int> a(n);

	for (int i = 0; i < n; i++)
		cin >> a[i];

	vector<int> b(a);

	if (prev_permutation(a.begin(), a.end())) {
		for (int i = 0; i < n - 1; i++)
			cout << a[i] << " ";
		cout << a[n - 1] << endl;
	}

	for (int i = 0; i < n - 1; i++)
		cout << b[i] << " ";
	cout << b[n - 1] << endl;

	if (next_permutation(b.begin(), b.end())) {
		for (int i = 0; i < n - 1; i++)
			cout << b[i] << " ";
		cout << b[n - 1] << endl;
	}

	return 0;
}