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 <vector>

using namespace std;

void print(vector<int> &v, bool b) {
  if (b) {
    cout << v[0];
    for (auto it = ++v.begin(); it != v.end(); ++it)
      cout << " " << *it;
    cout << endl;
  }
}

int main() {
  int n;
  cin >> n;
  vector<int> A, B, C;
  while (cin >> n)
    A.push_back(n);
  C = B = A;
  print(B, prev_permutation(B.begin(), B.end()));
  print(A, true);
  print(C, next_permutation(C.begin(), C.end()));
}