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(const std::vector<int>& v)
{
    for(int i = 0; i < v.size(); i++) {
        if(i) cout << " ";
        cout << v[i];
    }
    cout << endl;
}
int main(void){
    // Your code here!
    int n;
    cin >> n;
    vector<int> A(n);
    for(int i = 0; i < n; i++){
        cin >> A[i];
    }
    auto prev = A;
    if (prev_permutation(prev.begin(), prev.end())) {
        print(prev);
    }
    
    print(A);
    
    auto next = A;
    if (next_permutation(next.begin(), next.end())) {
        print(next);
    }
    return 0;
    
    
}