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.
#!/usr/bin/python3

import math
import os
import sys


DEBUG = 'DEBUG' in os.environ


def inp():
    return sys.stdin.readline().rstrip()


def dprint(*value, sep=' ', end='\n'):
    if DEBUG:
        print(*value, sep=sep, end=end)


def solve(N, M, G):
    A = {}

    for i in range(N):
        t = frozenset(G[i])
        if t not in A:
            A[t] = set([i])
        else:
            A[t].add(i)

    if len(A) != 3:
        return None

    (a1, v1), (a2, v2), (a3, v3) = A.items()
    v1 = frozenset(v1)
    v2 = frozenset(v2)
    v3 = frozenset(v3)

    if a1 != v2 | v3 or a2 != v3 | v1 or a3 != v1 | v2:
        return None

    ans = [0] * N
    for v in v1:
        ans[v] = 1
    for v in v2:
        ans[v] = 2
    for v in v3:
        ans[v] = 3
    return ans


def main():
    N, M = [int(e) for e in inp().split()]
    G = [[] for _ in range(N)]
    for _ in range(M):
        a, b = [int(e) - 1 for e in inp().split()]
        G[a].append(b)
        G[b].append(a)

    ans = solve(N, M, G)
    if not ans:
        print('-1')
    else:
        print(*ans)


if __name__ == '__main__':
    main()
