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 <vector>
#include <algorithm>

using namespace std;

void print_vector(vector<int> v, int n) {
  for(int i = 0; i < n - 1; i++) {
      cout << v[i] << " ";
  }
  cout << v[n - 1] << endl;
}

int main(void) {
  int n, m;
  cin >> n;
  vector<int> v;

  for(int i = 0; i < n; i++) {
    cin >> m;
    v.push_back(m);
  }

  vector<int> u(v);
  if(n == 1) {
    cout << v[0] << endl;
  }
  else {
    if(prev_permutation(v.begin(), v.end())) {
      print_vector(v, n);
    }
    
    print_vector(u, n);

    if(next_permutation(u.begin(), u.end())) {
      print_vector(u, n);
    }
  }

}