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.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.Scanner;
import java.util.Set;

public class CompleteTripartite {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);
    int numVertices = scanner.nextInt();
    long numEdges = scanner.nextLong();
    List<Set<Integer>> adjList = new ArrayList<>();
    List<Integer> groupIndex = new ArrayList<>();

    List<Set<Integer>> partition = new ArrayList<>();
    for (int i = 0; i < NUM_PARTITIONS_TRIPARTITE_GRAPH; i++) {
      partition.add(new HashSet<>());
    }

    for (int i = 0; i < numVertices; i++) {
      adjList.add(new HashSet<>());
      groupIndex.add(0);
    }

    for (long i = 0; i < numEdges; i++) {
      int v1 = scanner.nextInt();
      int v2 = scanner.nextInt();
      adjList.get(v1 - 1).add(v2 - 1);
      adjList.get(v2 - 1).add(v1 - 1);
    }

    for (int i = 0; i < numVertices; i++) {
      Set<Integer> toVertices = adjList.get(i);
      Set<Integer> excludedPartitions = new HashSet<>();

      for (Integer toVertex: toVertices) {
        for (int j = 0; j < NUM_PARTITIONS_TRIPARTITE_GRAPH; j++) {
          if (partition.get(j).contains(toVertex)) {
            excludedPartitions.add(j);
          }
        }
      }

      if (excludedPartitions.size() == 3) {
        System.out.println("-1");
        return;
      }

      for (int j = 0; j < NUM_PARTITIONS_TRIPARTITE_GRAPH; j++) {
        if (!excludedPartitions.contains(j)) {
          partition.get(j).add(i);
          groupIndex.set(i, j + 1);
          break;
        }
      }
    }

    for (int i = 0; i < NUM_PARTITIONS_TRIPARTITE_GRAPH; i++) {
      if (partition.get(i).isEmpty()) {
        System.out.println("-1");
        return;
      }
    }

    if (getNumEdgesExpected(partition) != numEdges) {
      System.out.println("-1");
      return;
    }

    for (int i = 0; i < numVertices; i++) {
      System.out.print(groupIndex.get(i) + " ");
    }
  }

  private static long getNumEdgesExpected(List<Set<Integer>> partition) {
    long group1Size = partition.get(0).size();
    long group2Size = partition.get(1).size();
    long group3Size = partition.get(2).size();
    return (group1Size * group2Size) + (group2Size * group3Size) + (group3Size * group1Size);
  }

  private static final int NUM_PARTITIONS_TRIPARTITE_GRAPH = 3;
}
