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<algorithm>
using namespace std;
int main() {
    int n, k = 0;
    cin >> n;
    int v[100000];
    for (int i = 0; i < n; i++)
        cin >> v[i];
    if (!prev_permutation(v, v + n)) {
        ++k;
        next_permutation(v, v + n);
    }
    for (int j = k; j < 3; j++) {
        for (int i = 0; i < n; i++) {
            cout << v[i];
            if (i != n - 1)cout << " ";
        }
        cout << endl;
        if (!next_permutation(v, v + n))
            break;
    }
}