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 JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.*;

public class Main {

	void solve (FastScanner in, PrintWriter out, Methods ms) {

		ArrayList<ArrayList<Integer>> bigList = new ArrayList<>();
		ArrayList<Integer> tempList = new ArrayList<>();
		ArrayList<Integer> list = new ArrayList<>();

		int n = in.nextInt();
		for (int i=0; i<n; i++) {
			int temp = in.nextInt();
			tempList.add(temp);
			list.add(temp);
		}

		Collections.sort(tempList);

		while (tempList.size() > 0) {
			ArrayList<Integer> a = new ArrayList<>();
			a.addAll(tempList);
			bigList.add(a);
			tempList = nextPermutation(tempList);
		}

		for (int i=0; i<bigList.size(); i++) {
			if (isSameList(list, bigList.get(i))) {

				if (i != 0) {
					printList(out, bigList.get(i-1));
				}

				printList(out, list);

				if (i != bigList.size()-1) {
					printList(out, bigList.get(i+1));
				}

			}
		}

	}

	static void printList (PrintWriter out, ArrayList<Integer> a) {
		for (int i=0; i<a.size(); i++) {
			out.print((i==0?"":" ")+a.get(i));
		}
		out.println();
	}

	static boolean isSameList (ArrayList<Integer> a, ArrayList<Integer> b) {
		for (int i=0; i<a.size(); i++) {
			if (a.get(i) != b.get(i)) return false;
		}
		return true;
	}

	static ArrayList<Integer> nextPermutation (ArrayList<Integer> list) {

		int pivotPos = -1;
		int pivot = 0;

		for (int i=list.size()-2; i>=0; i--) {
			if (list.get(i) < list.get(i+1)) {
				pivotPos = i;
				pivot = list.get(i);
				break;
			}
		}

		if (pivotPos==-1 && pivot==0) {
			list.clear();
			return list;
		}

		int L = pivotPos+1, R = list.size()-1, minPos = -1;
		int min = Integer.MAX_VALUE;
		for (int i=R; i>=L; i--) {
			if (pivot < list.get(i) && list.get(i) < min) {
				min = list.get(i);
				minPos = i;
			}
		}

		Collections.swap(list, pivotPos, minPos);
		Collections.sort(list.subList(L, R+1));

		return list;

	}



	public static void main(String[] args) {
		Main main = new Main();
		FastScanner in = new FastScanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		Methods ms = new Methods();
		main.solve(in, out, ms);
		in.close();
		out.close();
	}

	static class Methods {

		public void print (Object... ar) {System.out.println(Arrays.deepToString(ar));}

		public void yesno (PrintWriter out, boolean b) {out.println(b?"Yes":"No");}

		public void YESNO (PrintWriter out, boolean b) {out.println(b?"YES":"NO");}

		public int max (int... ar) {Arrays.sort(ar); return ar[ar.length-1];}

		public int min (int... ar) {Arrays.sort(ar); return ar[0];}

	}

	static class FastScanner {

		private InputStream in;
		private byte[] buffer = new byte[1024];
		private  int length = 0, p = 0;

		public FastScanner (InputStream stream) {
			in = stream;
		}

		public boolean hasNextByte () {
			if (p < length) return true;
			else {
				p = 0;
				try {length = in.read(buffer);}
				catch (Exception e) {e.printStackTrace();}
				if (length <= 0) return false;
			}
			return true;
		}

		public int readByte () {
			if (hasNextByte() == true) return buffer[p++];
			return -1;
		}

		public boolean isPrintable (int n) {return 33<=n&&n<=126;}

		public void skip () {
			while (hasNextByte() && !isPrintable(buffer[p])) p++;
		}

		public boolean hasNext () {skip(); return hasNextByte();}

		public String next () {
			if (!hasNext()) throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int t = readByte();
			while (isPrintable(t)) {
				sb.appendCodePoint(t);
				t = readByte();
			}
			return sb.toString();
		}

		public String[] nextArray (int n) {
			String[] ar = new String[n];
			for (int i=0; i<n; i++) ar[i] = next();
			return ar;
		}

		public int nextInt () {return Math.toIntExact(nextLong());}

		public int[] nextIntArray (int n) {
			int[] ar = new int[n];
			for (int i=0; i<n; i++) ar[i] = nextInt();
			return ar;
		}

		public long nextLong () {
			if (!hasNext()) throw new NoSuchElementException();
			boolean minus = false;
			int temp = readByte();
			if (temp == '-') {
				minus = true;
				temp = readByte();
			}
			if (temp<'0' || '9'<temp) throw new NumberFormatException();
			long n = 0;
			while (isPrintable(temp)) {
				if ('0'<=temp && temp<='9') {
					n *= 10;
					n += temp - '0';
				}
				else throw new NumberFormatException();
				temp = readByte();
			}
			return minus? -n : n;
		}

		public long[] nextLongArray (int n) {
			long[] ar = new long[n];
			for (int i=0; i<n; i++) ar[i] = nextLong();
			return ar;
		}

		public double nextDouble () {
			return Double.parseDouble(next());
		}

		public double[] nextDoubleArray (int n) {
			double[] ar = new double[n];
			for (int i=0; i<n; i++) ar[i] = nextDouble();
			return ar;
		}

		public void close () {
			try {in.close();}
			catch(Exception e){}
		}

	}

}