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;
#define long int64_t

template<class T>
inline istream& operator >>( istream& s, vector<T>& v ) {
	for( size_t i = 0; i < v.size(); ++i ) { s >> v[i]; }
	return s;
}

template<class T>
inline ostream& operator <<( ostream& s, vector<T>& v ) {
	for( size_t i = 0; i < v.size(); ++i ) {
		if( i ) { s << ' '; }
		s << v[i];
	}
	return s;
}

int main() {
	ios_base::sync_with_stdio( false );

	int n;
	cin >> n;
	vector<int> a( n ), b, c;
	cin >> a;
	b = a;
	c = a;
	if( prev_permutation( a.begin(), a.end() ) ) { cout << a << endl; }
	cout << b << endl;
	if( next_permutation( c.begin(), c.end() ) ) { cout << c << endl; }

	return 0;
}