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>
#include<vector>
using namespace std;
int main() {
  int n;
  cin >> n;
  vector<int> a(n),b(n),c(n);
  for(int i=0; i<n; i++) {
      cin >> a[i];
      b[i]=a[i];
      c[i]=a[i];
  }
  if(prev_permutation(b.begin(),b.end())) {
      for(int i=0; i<n; i++) {
          if(i>0) {
              cout << " ";
          }
          cout << b[i];
      }
      cout << endl;
  }
  for(int i=0; i<n; i++) {
      if(i>0) {
          cout << " ";
      }
      cout << a[i];
  }
  cout << endl;
  if(next_permutation(c.begin(),c.end())) {
      for(int i=0; i<n; i++) {
          if(i>0) {
              cout << " ";
          }
          cout << c[i];
      }
      cout << endl;
  }
}