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.
try:
    from string_source import string_source
except ImportError:
    source = input

from collections import defaultdict


def complete_bipartite(n, edges):
    if not edges:
        return False

    neighbors = defaultdict(set, {})

    for e1, e2 in edges:
        neighbors[e1].add(e2)
        neighbors[e2].add(e1)

    s1, s2 = edges[0]

    groups = [None, None, None]
    groups[2] = neighbors[s1].intersection(neighbors[s2])
    groups[1] = neighbors[s1].difference(neighbors[s2])
    groups[0] = set(neighbors).difference(groups[2], groups[1])

    def get_group(node):
        return next(idx for idx, g in enumerate(groups) if node in g)

    sizes = [len(g) for g in groups]

    if sum(len(g) for g in groups) < n:
        return False
    if any(len(g) == 0 for g in groups):
        return False

    for e1, e2 in edges:
        if get_group(e1) == get_group(e2):
            return False

    answer = [0] * n
    for node, neigh in neighbors.items():
        g = get_group(node)
        if sum(s for idx, s in enumerate(sizes) if idx != g) != len(neigh):
            return False

        answer[node - 1] = g + 1

    return answer


def answer(source):
    n, m = map(int, source().strip().split())
    edges = [[int(k) for k in source().strip().split()] for _ in range(m)]

    a = complete_bipartite(n, edges)
    if not a:
        print(-1)
    else:
        print(" ".join(map(str, a)))


answer(input)

if False:
    answer(
        string_source(
            """6 11
    1 2
    1 3
    1 4
    1 5
    1 6
    2 4
    2 5
    2 6
    3 4
    3 5
    3 6"""
        )
    )

    answer(
        string_source(
            """4 6
    1 2
    1 3
    1 4
    2 3
    2 4
    3 4"""
        )
    )
