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(int a[], int n){
    for(int i=0; i<n-1; i++){
        cout << a[i] << " ";
    }
    cout << a[n-1] << endl;
}

int main(){
    int n;
    cin >> n;
    int a[10];
    for(int i=0; i<n; i++){
        cin >> a[i];
    }
    if(prev_permutation(a, a+n)){
        print(a, n);
    }
    next_permutation(a, a+n);
    print(a, n);
    if(next_permutation(a, a+n)){
        print(a, n);
    }
    return 0;
}