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>a,b,c;
int n;
int main()
{
	cin>>n;
	for(int i=0;i<n;i++)
	{
		int k;cin>>k;
		a.push_back(k);
		b.push_back(k);
		c.push_back(k);
	}
	if(prev_permutation(b.begin(),b.end()))
	{
		for(int i=0;i<n;i++)cout<<(i?" ":"")<<b[i];
		cout<<endl;
	}
	for(int i=0;i<n;i++)cout<<(i?" ":"")<<a[i];
	cout<<endl;
	if(next_permutation(c.begin(),c.end()))
	{
		for(int i=0;i<n;i++)cout<<(i?" ":"")<<c[i];
		cout<<endl;
	}
}