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.
n,m=map(int,input().split())
EE=[]
if m<3:
  print(-1)
else:
  edge = [[] for i in range(n)]
  a,b=map(int,input().split())
  edge[a-1].append(b-1)
  edge[b-1].append(a-1)
  EE.append([a-1,b-1])

  for i in range(m-1):
    x,y=map(int,input().split())
    edge[x-1].append(y-1)
    edge[y-1].append(x-1)
    EE.append([x-1,y-1])
  c=0  
  for i in range(n):
    if a-1 in edge[i] and b-1 in edge[i]:
      c=i+1
      break
  if c==0:
    print(-1)
  else:
    Ans=[0]*n
    Ans[a-1]=1
    Ans[b-1]=2
    Ans[c-1]=3
    flg=True
    C=[1]*3
    for i in range(n):
      if Ans[i]!=0:
        continue
      else:
        E=edge[i]
        if a-1 in E and b-1 in E and c-1 not in E:
          Ans[i]=3
          C[2]+=1
        elif a-1 in E and b-1 not in E and c-1 in E:
          Ans[i]=2
          C[1]+=1
        elif a-1 not in E and b-1 in E and c-1 in E:
          Ans[i]=1
          C[0]+=1
        else:
          print(-1)
          flg=False
          break
    if flg:
      T=[0]*3
      for x,y in EE:
        xx,yy=Ans[x],Ans[y]
        if xx==yy:
          print(-1)
          flg=False
          break
        elif xx==1 and yy==2:
          T[0]+=1
        elif xx==2 and yy==1:
          T[0]+=1
        elif xx==1 and yy==3:
          T[1]+=1
        elif xx==3 and yy==1:
          T[1]+=1
        else:
          T[2]+=1
    if flg:
      if T[0]==C[0]*C[1] and T[1]==C[0]*C[2] and T[2]==C[1]*C[2]:
        print(*Ans)
      else:
        print(-1)





  