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 printVec(vector<int> &vec)
{
    for(int i = 0; i < vec.size(); ++i)
      cout << (i == 0 ? "" : " ") << vec[i];
    cout << endl;
}

int main()
{
    int N;
    cin >> N;
    vector<int> A(N);
    
    for(int i = 0; i < N; ++i)
      cin >> A[i];
    
    vector<int> B = A;
    
    if(prev_permutation(B.begin(), B.end()))
        printVec(B);
        
    printVec(A);
    
    B = A;
    if(next_permutation(B.begin(), B.end()))
        printVec(B);
    
    return 0;
    
}