You have a simple undirected graph consisting of n vertices and m edges. The graph doesn't contain self-loops, there is at most one edge between a pair of vertices. The given graph can be disconnected.

Let's make a definition.

Let v_1 and v_2 be two some nonempty subsets of vertices that do not intersect. Let f(v_{1}, v_{2}) be true if and only if all the conditions are satisfied:

  1. There are no edges with both endpoints in vertex set v_1. 
  2. There are no edges with both endpoints in vertex set v_2. 
  3. For every two vertices x and y such that x is in v_1 and y is in v_2, there is an edge between x and y. 



Create three vertex sets (v_{1}, v_{2}, v_{3}) which satisfy the conditions below;

  1. All vertex sets should not be empty. 
  2. Each vertex should be assigned to only one vertex set. 
  3. f(v_{1}, v_{2}), f(v_{2}, v_{3}), f(v_{3}, v_{1}) are all true. 



Is it possible to create such three vertex sets? If it's possible, print matching vertex set for each vertex.

Input

The first line contains two integers n and m (3 ≤ n ≤ 10^{5}, 0 ≤ m ≤ min(3 ⋅ 10^{5}, (n(n-1))/(2))) — the number of vertices and edges in the graph.

The i-th of the next m lines contains two integers a_{i} and b_{i} (1 ≤ a_{i} < b_{i} ≤ n) — it means there is an edge between a_{i} and b_{i}. The graph doesn't contain self-loops, there is at most one edge between a pair of vertices. The given graph can be disconnected.

Output

If the answer exists, print n integers. i-th integer means the vertex set number (from 1 to 3) of i-th vertex. Otherwise, print -1.

If there are multiple answers, print any.

Examples

Input


6 11
1 2
1 3
1 4
1 5
1 6
2 4
2 5
2 6
3 4
3 5
3 6


Output


1 2 2 3 3 3 

Input


4 6
1 2
1 3
1 4
2 3
2 4
3 4


Output


-1

Note

In the first example, if v_{1} = \{ 1 \}, v_{2} = \{ 2, 3 \}, and v_{3} = \{ 4, 5, 6 \} then vertex sets will satisfy all conditions. But you can assign vertices to vertex sets in a different way; Other answers like "2 3 3 1 1 1" will be accepted as well.

<image>

In the second example, it's impossible to make such vertex sets.
import java.io.*;
import java.util.*;

public class SolutionD {

    private static BufferedWriter bufferedWriter = new BufferedWriter(new OutputStreamWriter(System.out));

    public static void main(String[] args) throws IOException {
        Reader reader = new Reader();
        int[] nm = reader.readIntNumbers();
        int n = nm[0];
        int m = nm[1];

        Map<Integer, List<Integer>> graph = new HashMap<>();
        for (int i = 0; i < m; i++) {
            int[] edge = reader.readIntNumbers();
            graph.putIfAbsent(edge[0], new ArrayList<>());
            graph.putIfAbsent(edge[1], new ArrayList<>());

            graph.get(edge[0]).add(edge[1]);
            graph.get(edge[1]).add(edge[0]);
        }

        int[] vertexesBySets = new int[n + 1];

        // ------
        int firstVertex = getFirstUnusedVertex(vertexesBySets);
        if(!graph.containsKey(firstVertex)) {
            System.out.print("-1");
            return;
        }
        Set<Integer> firstVertexNeighbors = new HashSet<>(graph.get(firstVertex));

        Set<Integer> possibleSet = new HashSet<>();
        for (int i = 1; i <= n; i++) {
            if (!firstVertexNeighbors.contains(i)) {
                vertexesBySets[i] = 1;
                possibleSet.add(i);
            }
        }

        if(!doVertexesBelongToSameSet(possibleSet, graph, firstVertexNeighbors)) {
            System.out.print("-1");
            return;
        }

        // ------
        firstVertex = getFirstUnusedVertex(vertexesBySets);
        if(!graph.containsKey(firstVertex)) {
            System.out.print("-1");
            return;
        }
        firstVertexNeighbors = new HashSet<>(graph.get(firstVertex));

        possibleSet = new HashSet<>();
        for (int i = 1; i <= n; i++) {
            if (!firstVertexNeighbors.contains(i)) {
                vertexesBySets[i] = 2;
                possibleSet.add(i);
            }
        }

        if(!doVertexesBelongToSameSet(possibleSet, graph, firstVertexNeighbors)) {
            System.out.print("-1");
            return;
        }

        // ------
        firstVertex = getFirstUnusedVertex(vertexesBySets);
        if(!graph.containsKey(firstVertex)) {
            System.out.print("-1");
            return;
        }
        firstVertexNeighbors = new HashSet<>(graph.get(firstVertex));

        possibleSet = new HashSet<>();
        for (int i = 1; i <= n; i++) {
            if (!firstVertexNeighbors.contains(i)) {
                vertexesBySets[i] = 3;
                possibleSet.add(i);
            }
        }

        if(!doVertexesBelongToSameSet(possibleSet, graph, firstVertexNeighbors)) {
            System.out.print("-1");
            return;
        }

        // ------
        for(int i = 1; i < vertexesBySets.length; i++) {
            if(vertexesBySets[i] == 0) {
                System.out.print("-1");
                return;
            }
        }


        for(int i = 1; i < vertexesBySets.length; i++) {
            bufferedWriter.write(vertexesBySets[i] + " ");
        }
        bufferedWriter.flush();

    }

    private static int getFirstUnusedVertex(int[] vertexesBySets) {
        for(int i = 1; i < vertexesBySets.length; i++) {
            if(vertexesBySets[i] == 0) {
                return i;
            }
        }
        return -1;
    }

    private static boolean doVertexesBelongToSameSet(Set<Integer> possibleSet,
                                                     Map<Integer, List<Integer>> graph,
                                                     Set<Integer> mainVertexNeighbors) {
        for (int currVertex : possibleSet) {
            if(!graph.containsKey(currVertex)) {
                return false;
            }
            List<Integer> neighbors = graph.get(currVertex);
            if(neighbors.size() != mainVertexNeighbors.size()) {
                return false;
            }
            for (int neighbor : neighbors) {
                if (!mainVertexNeighbors.contains(neighbor)) {
                    return false;
                }
            }
        }
        return true;
    }

}

class Reader {

    BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));

    public StringTokenizer getStringTokenizer() throws IOException {
        String line = bufferedReader.readLine().replaceAll("\\s+$", "");
        return new StringTokenizer(line, " ");
    }

    public int getNextInt(StringTokenizer stringTokenizer) {
        while (stringTokenizer.hasMoreTokens()) {
            return Integer.parseInt(stringTokenizer.nextToken());
        }
        throw new RuntimeException("no more tokens in string");
    }

    public long getNextLong(StringTokenizer stringTokenizer) {
        while (stringTokenizer.hasMoreTokens()) {
            return Long.parseLong(stringTokenizer.nextToken());
        }
        throw new RuntimeException("no more tokens in string");
    }

    public String getNextString(StringTokenizer stringTokenizer) {
        while (stringTokenizer.hasMoreTokens()) {
            return stringTokenizer.nextToken();
        }
        throw new RuntimeException("no more tokens in string");
    }


    public String readStringValue() throws IOException {
        return bufferedReader.readLine().replaceAll("\\s+$", "");
    }

    public int readIntValue() throws IOException {
        String line = bufferedReader.readLine().replaceAll("\\s+$", "");
        int parsedToInt = Integer.parseInt(line);
        return parsedToInt;
    }

    public int[] readIntNumbers() throws IOException {
        String[] line = bufferedReader.readLine().replaceAll("\\s+$", "").split(" ");
        int[] parsedToInt = Arrays.stream(line).mapToInt(Integer::parseInt).toArray();
        return parsedToInt;
    }

    public long readLongValue() throws IOException {
        String line = bufferedReader.readLine().replaceAll("\\s+$", "");
        long parsedToLong = Long.parseLong(line);
        return parsedToLong;
    }

    public long[] readLongNumbers() throws IOException {
        String[] line = bufferedReader.readLine().replaceAll("\\s+$", "").split(" ");
        long[] parsedToLong = Arrays.stream(line).mapToLong(Long::parseLong).toArray();
        return parsedToLong;
    }


}