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 CompleteTripartite {
    static HashSet<Integer>[] graph;
    public static void main(String[] args) {
        FastScanner scanner = new FastScanner();
        PrintWriter out = new PrintWriter(System.out,false);
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        graph = new HashSet[n];
        for(int i = 0; i < n; i++) graph[i] = new HashSet<>();
        for(int i = 0; i < m; i++) {
            int u = scanner.nextInt()-1, v = scanner.nextInt()-1;
            graph[u].add(v);
            graph[v].add(u);
        }
        int[] mapping = new int[n];
        for(int col = 1; col < 4; col++) {
            for(int i = 0; i< n; i++) {
                if (mapping[i] == 0) {
                    mapping[i]=  col;
                    for(int j = 0; j < n; j++) {
                        if (j == i) continue;
                        if (!graph[i].contains(j)) {
                            if (mapping[j] == 0) {
                                mapping[j] = col;
                            }
                            else {
                                System.out.println(-1);
                                return;
                            }
                        }
                    }
                    break;
                }
            }
        }
        for(int i = 0; i < n; i++) {
            for(int edge: graph[i]) {
                if (mapping[i] == mapping[edge]) {
                    System.out.println(-1);
                    return;
                }
            }
        }
        int[] cnt = new int[4];
        for(int i = 0; i < n; i++) {
           cnt[mapping[i]]++;
        }
        if (cnt[1] == 0 || cnt[2] == 0 || cnt[3] == 0 || cnt[0] > 0) {
            System.out.println(-1);
            return;
        }
        long tot = (long)cnt[1] * cnt[2] + (long)cnt[2] * cnt[3] + (long)cnt[1] * cnt[3];
        if (tot != m) {
            System.out.println(-1);
            return;
        }
        for(int i = 0; i < n; i++) {
            if (i > 0) out.print(" ");
            out.print(mapping[i]);
        }
        out.println();
        out.flush();
    }
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }
        public FastScanner() {
            this(new InputStreamReader(System.in));
        }
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
        String readNextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}
