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 <ostream>

void print_array(const int a[], int n) {
  for (int i = 0; i < n; ++i) {
    if (i > 0)
      std::cout << " ";
    std::cout << a[i];
  }
  std::cout << std::endl;
}

int main(int argc, char *argv[]) {
  int n;
  std::cin >> n;
  int a[10];
  for (int i = 0; i < n; ++i)
    std::cin >> a[i];

  if (std::prev_permutation(a, a + n))
    print_array(a, n);
  std::next_permutation(a, a + n);
  print_array(a, n);
  if (std::next_permutation(a, a + n))
    print_array(a, n);
}