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;

template<class T>
ostream& operator<<(ostream& os,vector<T> const& v){for(auto itr=v.begin();itr!=v.end();++itr){if(itr!=v.begin())os<<' ';os<<*itr;}return os;}

signed main(){

  int N;
  cin>>N;
  vector<int> a(N);
  for(auto& ai:a)cin>>ai;
  
  auto p = a;
  auto n = a;

  if(prev_permutation(p.begin(),p.end()))cout<<p<<endl;
  cout<<a<<endl;
  if(next_permutation(n.begin(),n.end()))cout<<n<<endl;

}