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>
using namespace std;
int main(){
	int n;
	cin>>n;
	int a[n],b[n];
	for(int i=0; i<n; i++){
		cin>>a[i];
		b[i]=a[i];
	}
	if(prev_permutation(a, a+n)){
		//prev_permutation(a, a+n);
		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, b+n)){
		//next_permutation(b, b+n);
		for(int i=0; i<n-1; i++)
			cout<<b[i]<<" ";
		cout<<b[n-1]<<endl;
	}
	return 0;
}