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;
typedef vector<int>V;
int main(void){
	int n;
	V v;
	int x;
	int i;
	cin>>n;
	for(i=0;i<n;i++)	cin>>x,v.push_back(x);
	if(prev_permutation(v.begin(),v.end())){
		for(i=0;i<(int)v.size();i++){
			if(i)	cout<<" ";
			cout<<v[i];
		}
		cout<<endl;
	}
	next_permutation(v.begin(),v.end());
	for(i=0;i<(int)v.size();i++){
		if(i)	cout<<" ";
		cout<<v[i];
	}
	cout<<endl;
	if(next_permutation(v.begin(),v.end())){
		for(i=0;i<(int)v.size();i++){
			if(i)	cout<<" ";
			cout<<v[i];
		}
		cout<<endl;
	}
	return 0;
}