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<tuple>
#include<vector>
#include<queue>
#include<algorithm>
using namespace std;

#define INF ((int)(1e9))
#define MAX 11

int n, p[MAX],t[MAX];
bool hoge(int a[], int b[]){
	priority_queue<int, vector<int>, greater<int>> Q;
	int num = -1, next = INF;
	for(int i = n-2; i >= 0; i--){
		if(a[i] < a[i+1]){
			num = i;
			break;
		}
	}
	if(num == -1) return false;
	
	for(int i = n-1; i > num; i--){
		if(a[num] < a[i])next = min(a[i],next);
	}
	for(int i = n-1; i >= num; i--){
		if(a[i] != next) Q.push(a[i]);
	}
	
	for(int i = 0; i < num; i++){
		b[i] = a[i];
	}
	
	b[num] = next;
	
	for(int i = num+1; i < n; i++){
		b[i] = Q.top(); Q.pop();
	}
	return true;
}

bool fuga(int a[], int b[]){
	priority_queue<int, vector<int>> Q;
	int num = -1, next = -INF;
	for(int i = n-2; i >= 0; i--){
		if(a[i] > a[i+1]){
			num = i;
			break;
		}
	}
	if(num == -1) return false;
	
	for(int i = n-1; i > num; i--){
		if(a[num] > a[i])next = max(a[i],next);
	}
	for(int i = n-1; i >= num; i--){
		if(a[i] != next) Q.push(a[i]);
	}
	
	for(int i = 0; i < num; i++){
		b[i] = a[i];
	}
	
	b[num] = next;
	
	for(int i = num+1; i < n; i++){
		b[i] = Q.top(); Q.pop();
	}
	return true;
}

void p_array(int a[]){
	for(int i = 0; i < n; i++){
		cout<<(i?" ":"")<<a[i];
	}
	cout<<endl;
}

int main(){
	cin>>n;
	
	for(int i = 0; i < n; i++){
		cin>>p[i];
	}
	if(fuga(p,t)) p_array(t);
	
	p_array(p);
	
	if(hoge(p,t)) p_array(t);
	
	return 0;
}