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>

void print(int* A, int n)
{
	std::cout << A[0];
	for (int i=1; i<n; i++) std::cout << " " << A[i];
	std::cout << std::endl;
}

int main()
{
	int n; std::cin >> n;
	
	int* A = new int[n];
	std::string buf;
	for (int i=0; i<n; i++) std::cin >> A[i];
	
	int* B = new int[n];
	for (int i=0; i<n; i++) B[i] = A[i];

	if (std::prev_permutation(A, A+n)) print(A, n);
	print(B, n);
	if (std::next_permutation(B, B+n)) print(B, n);
	
	delete[] A;
	delete[] B;
	
	return 0;
}