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 Vec = std::vector<int>;

void print_vec(Vec vec) {
    for (auto iter = vec.begin(); iter != vec.end(); ++iter) {
        std::cout << *iter;
        if (iter != vec.end() - 1) std::cout << ' ';
    }
    std::cout << std::endl;
}

int main(void) {
    int n;
    std::cin >> n;

    Vec vec{};
    for (int i = 0; i < n; ++i) {
        int a;
        std::cin >> a;
        vec.push_back(a);
    }
    Vec vec0(vec);

    if (std::prev_permutation(vec.begin(), vec.end())) print_vec(vec);
    print_vec(vec0);
    if (std::next_permutation(vec0.begin(), vec0.end())) print_vec(vec0);
}