Problem: Recently, Pari and Arya did some research about NP-Hard problems and they found the minimum vertex cover problem very interesting.

Suppose the graph G is given. Subset A of its vertices is called a vertex cover of this graph, if for each edge uv there is at least one endpoint of it in this set, i.e. <image> or <image> (or both).

Pari and Arya have won a great undirected graph as an award in a team contest. Now they have to split it in two parts, but both of them want their parts of the graph to be a vertex cover.

They have agreed to give you their graph and you need to find two disjoint subsets of its vertices A and B, such that both A and B are vertex cover or claim it's impossible. Each vertex should be given to no more than one of the friends (or you can even keep it for yourself).

Input

The first line of the input contains two integers n and m (2 ≤ n ≤ 100 000, 1 ≤ m ≤ 100 000) — the number of vertices and the number of edges in the prize graph, respectively.

Each of the next m lines contains a pair of integers ui and vi (1 ≤ ui, vi ≤ n), denoting an undirected edge between ui and vi. It's guaranteed the graph won't contain any self-loops or multiple edges.

Output

If it's impossible to split the graph between Pari and Arya as they expect, print "-1" (without quotes).

If there are two disjoint sets of vertices, such that both sets are vertex cover, print their descriptions. Each description must contain two lines. The first line contains a single integer k denoting the number of vertices in that vertex cover, and the second line contains k integers — the indices of vertices. Note that because of m ≥ 1, vertex cover cannot be empty.

Examples

Input

4 2
1 2
2 3


Output

1
2 
2
1 3 


Input

3 3
1 2
2 3
1 3


Output

-1

Note

In the first sample, you can give the vertex number 2 to Arya and vertices numbered 1 and 3 to Pari and keep vertex number 4 for yourself (or give it someone, if you wish).

In the second sample, there is no way to satisfy both Pari and Arya.

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.math.BigInteger;
import java.util.InputMismatchException;
import java.util.ArrayList;
import java.util.List;

public class C
{
	private static boolean visited[];
	private static color colors[];
	private static Graph g;
	private static boolean flag = false;
	private static int redNodes = 0, greenNodes = 0;

	public static void main(String args[])
	{
		FastReader in = new FastReader(System.in);
		int n = in.nextInt();
		int m = in.nextInt();
		int i;

		visited = new boolean[n];
		colors = new color[n];

		for (i = 0; i < n; i++)
			colors[i] = color.White;
		g = new Graph(n);

		for (i = 0; i < m; i++)
		{
			int u = in.nextInt();
			int v = in.nextInt();

			g.adj[u - 1].add(v - 1);
			g.adj[v - 1].add(u - 1);
		}

		dfs(n);

		if (flag)
			System.out.println("-1");
		else
		{
			System.out.println(redNodes);
			for (i = 0; i < n; i++)
				if (colors[i] == color.Red)
					System.out.print((i + 1) + " ");
			System.out.println();

			System.out.println(greenNodes);
			for (i = 0; i < n; i++)
				if (colors[i] == color.Green)
					System.out.print((i + 1) + " ");
			System.out.println();

			// for (i = 0; i < n; i++)
			// System.out.println((i + 1) + " " + colors[i]);
		}
	}

	static class Graph
	{
		private List<Integer>[] adj;

		public Graph(int n)
		{
			adj = new List[n];
			for (int i = 0; i < n; i++)
				adj[i] = new ArrayList<Integer>();
		}
	}

	private static enum color
	{
		White, Red, Green
	};

	private static void dfs(int n)
	{
		for (int i = 0; i < n; i++)
			if (!visited[i] && !flag)
			{
				colors[i] = color.Red;
				// System.out.println("setting color of node " + (i + 1) + " = " + color.Red);
				redNodes++;
				// System.out.println("**" + i);
				dfsVisit(i, color.Red);
			}
	}

	private static void dfsVisit(int i, color nodeColor)
	{
		if (flag)
			return;

		visited[i] = true;

		List<Integer> neighbours = g.adj[i];
		for (Integer neighbour : neighbours)
		{
			if (!visited[neighbour])
			{
				color neighbourColor = findAntiColor(nodeColor);
				if (neighbourColor == color.Red)
					redNodes++;
				else
					greenNodes++;

				colors[neighbour] = neighbourColor;
				// System.out.println("setting color of node " + (neighbour + 1) + " = " + neighbourColor);
				dfsVisit(neighbour, neighbourColor);
			}
			else
			{
				if (colors[neighbour] == nodeColor)
				{
					flag = true;
					return;
				}
			}
		}
	}

	private static color findAntiColor(color c)
	{
		if (c == color.Green)
			return color.Red;
		else
			return color.Green;
	}
}

class FastReader
{
	private boolean finished = false;

	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;

	public FastReader(InputStream stream)
	{
		this.stream = stream;
	}

	public int read()
	{
		if (numChars == -1)
		{
			throw new InputMismatchException();
		}
		if (curChar >= numChars)
		{
			curChar = 0;
			try
			{
				numChars = stream.read(buf);
			}
			catch (IOException e)
			{
				throw new InputMismatchException();
			}
			if (numChars <= 0)
			{
				return -1;
			}
		}
		return buf[curChar++];
	}

	public int peek()
	{
		if (numChars == -1)
		{
			return -1;
		}
		if (curChar >= numChars)
		{
			curChar = 0;
			try
			{
				numChars = stream.read(buf);
			}
			catch (IOException e)
			{
				return -1;
			}
			if (numChars <= 0)
			{
				return -1;
			}
		}
		return buf[curChar];
	}

	public int nextInt()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-')
		{
			sgn = -1;
			c = read();
		}
		int res = 0;
		do
		{
			if (c == ',')
			{
				c = read();
			}
			if (c < '0' || c > '9')
			{
				throw new InputMismatchException();
			}
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public long nextLong()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-')
		{
			sgn = -1;
			c = read();
		}
		long res = 0;
		do
		{
			if (c < '0' || c > '9')
			{
				throw new InputMismatchException();
			}
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public String nextString()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do
		{
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	public boolean isSpaceChar(int c)
	{
		if (filter != null)
		{
			return filter.isSpaceChar(c);
		}
		return isWhitespace(c);
	}

	public static boolean isWhitespace(int c)
	{
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	private String readLine0()
	{
		StringBuilder buf = new StringBuilder();
		int c = read();
		while (c != '\n' && c != -1)
		{
			if (c != '\r')
			{
				buf.appendCodePoint(c);
			}
			c = read();
		}
		return buf.toString();
	}

	public String nextLine()
	{
		String s = readLine0();
		while (s.trim().length() == 0)
			s = readLine0();
		return s;
	}

	public String nextLine(boolean ignoreEmptyLines)
	{
		if (ignoreEmptyLines)
		{
			return nextLine();
		}
		else
		{
			return readLine0();
		}
	}

	public BigInteger nextBigInteger()
	{
		try
		{
			return new BigInteger(nextString());
		}
		catch (NumberFormatException e)
		{
			throw new InputMismatchException();
		}
	}

	public char nextCharacter()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		return (char) c;
	}

	public double nextDouble()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-')
		{
			sgn = -1;
			c = read();
		}
		double res = 0;
		while (!isSpaceChar(c) && c != '.')
		{
			if (c == 'e' || c == 'E')
			{
				return res * Math.pow(10, nextInt());
			}
			if (c < '0' || c > '9')
			{
				throw new InputMismatchException();
			}
			res *= 10;
			res += c - '0';
			c = read();
		}
		if (c == '.')
		{
			c = read();
			double m = 1;
			while (!isSpaceChar(c))
			{
				if (c == 'e' || c == 'E')
				{
					return res * Math.pow(10, nextInt());
				}
				if (c < '0' || c > '9')
				{
					throw new InputMismatchException();
				}
				m /= 10;
				res += (c - '0') * m;
				c = read();
			}
		}
		return res * sgn;
	}

	public boolean isExhausted()
	{
		int value;
		while (isSpaceChar(value = peek()) && value != -1)
			read();
		return value == -1;
	}

	public String next()
	{
		return nextString();
	}

	public SpaceCharFilter getFilter()
	{
		return filter;
	}

	public void setFilter(SpaceCharFilter filter)
	{
		this.filter = filter;
	}

	public interface SpaceCharFilter
	{
		public boolean isSpaceChar(int ch);
	}
}

class Obj implements Comparable<Obj>
{
	char c;
	int size;

	public Obj(char c, int size)
	{
		this.c = c;
		this.size = size;
	}

	public int compareTo(Obj that)
	{
		if (this.size > that.size)
		{
			return -1;
		}
		else if (this.size < that.size)
		{
			return 1;
		}
		else
		{
			if (this.c < that.c)
			{
				return -1;
			}
			else if (this.c > that.c)
			{
				return 1;
			}
			else
			{
				return 0;
			}
		}
	}
}