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 <algorithm>
#include<iostream>
#include<vector>
#include<deque>
#include<queue>
#include<list>
#include<stack>
#include<map>
#include<set>
#include<string>
#include <sstream>

#include<stdlib.h>
#include<string.h>
#include<math.h>
#include<limits.h>

using namespace std;


int main(){
  long ii,jj,kk;

  vector<int> a,a2;
  vector<int> prev;
  int n;

  cin >> n;

  a.resize(n);
  a2.resize(n);
  prev.resize(n);
  for(ii=0;ii<n;ii++){
    cin >> a[ii];
  }

  copy(a.begin(),a.end(),a2.begin());

  sort(a2.begin(),a2.end());
  bool flg;
  do{
    flg = false;

    for(ii=0;ii<n;ii++){
      if(a[ii] != a2[ii]){
        break;
      }
    }
    if(ii == n){
      break;
    }
    
    //for(auto val :a2){
    //  cout << val << " " ;
    //}
    //cout << endl;
    
    copy(a2.begin(),a2.end(),prev.begin());
    
  }while(next_permutation(a2.begin(),a2.end()));

  if(prev[0] != 0){

    for(ii=0;ii<n;ii++){
      cout << prev[ii];
      if(ii != n-1){
        cout << " ";
      }
      else{
        cout << endl;
      }
    }
    
  }
  for(ii=0;ii<n;ii++){
    cout << a[ii];
    if(ii != n-1){
      cout << " ";
    }
    else{
      cout << endl;
    }
  }

  if(next_permutation(a2.begin(),a2.end())){
    for(ii=0;ii<n;ii++){
      cout << a2[ii];
      if(ii != n-1){
        cout << " ";
      }
      else{
        cout << endl;
      }    
    }
  }
  
  return 0;
}