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.*;
import java.io.*;

public class D {
    public static void main(String[] args) throws IOException {
        FastScanner input = new FastScanner(System.in);
        PrintWriter output = new PrintWriter(System.out);

        int n = input.nextInt(), m = input.nextInt();
        ArrayList<ArrayList<Integer>> list = new ArrayList<>();
        for (int i = 0; i < n; i++)
            list.add(new ArrayList<>());

        for (int i = 0; i < m; i++) {
            int u = input.nextInt() - 1;
            int v = input.nextInt() - 1;
            list.get(u).add(v);
            list.get(v).add(u);
        }

        int[] groups = new int[n];
        int[] sizes = new int[n];
        sizes[0] = n;

        int group = 0;
        boolean correct = true;
        for (int i = 0; i < n; i++) {
            boolean find = false;
            ArrayList<Integer> vertices = list.get(i);
            for (Integer vertice : vertices) {
                if (groups[i] == groups[vertice]) {
                    sizes[groups[vertice]]--;
                    sizes[group + 1]++;
                    groups[vertice] = group + 1;
                    find = true;
                }
            }
            if (find)
                group++;
        }

        if (group != 2)
            correct = false;

        // output.println(Arrays.toString(sizes));
        for (int i = 0; i < n; i++)
            if (sizes[groups[i]] != n - list.get(i).size())
                correct = false;

        if (!correct)
            output.println("-1");
        else {
            for (int i = 0; i < n - 1; i++)
                output.print((groups[i] + 1) + " ");
            output.println(groups[n - 1] + 1);
        }

        output.close();
    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        FastScanner(FileReader s) {
            br = new BufferedReader(s);
        }

        String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        String nextLine() throws IOException {
            return br.readLine();
        }

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

        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        long nextLong() throws IOException {
            return Long.parseLong(next());
        }
    }
}