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;
void print(vector<int> v) {
  for (size_t i = 0; i < v.size(); i++) {
    if (i) cout << " ";
    cout << v[i];
  }
  cout << endl;
}
int main() {
  int n;
  cin >> n;
  vector<int> a(n);
  for (auto &p : a) cin >> p;
  vector<int> b(a), c(a);
  prev_permutation(b.begin(), b.end());
  next_permutation(c.begin(), c.end());
  if (b < a) print(b);
  print(a);
  if (c > a) print(c);
  return 0;
}