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.

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In the second example, it's impossible to make such vertex sets.


def main():
    vertex, edge = map(int, input().split())
    data = {key : set() for key in range(1, vertex + 1)}
    for i in range(edge):
        a, b = map(int, input().split())
        data[a].add(b)
        data[b].add(a)
    v = []
    temp = [None, None, None]
    for node in data.values():
        if temp[0] and temp[1] and temp[2]:
            break
        elif temp[0] is None:
            temp[0] = node
        elif temp[1] is None and node != temp[0]:
            temp[1] = node
        elif temp[2] is None and node != temp[1] and node != temp[0]:
            temp[2] = node
    dec = False
    if temp[0] and temp[1] and temp[2]:
        for i in range(1, vertex + 1):
            if data[i] == temp[0]:
                v.append(1)
            elif data[i] == temp[1]:
                v.append(2)
            elif data[i] == temp[2]:
                v.append(3)
            else:
                dec = True
                break
    else:
        dec = True
    if dec:
        print(-1)
    else:
        for team in v:
            print(team , end = ' ')





if __name__ == '__main__':
    main()
