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.
from sys import stdin
input = stdin.readline
v, e = map(int,input().split())
d = {}
for i in range(1, v+1):
	d[i] = []
for ed in range(e):
	a,b = map(int,input().split())
	d[a].append(b)
	d[b].append(a)
for i in d:
	d[i].sort()
sas = {}
for i in d:
	sas[tuple(d[i])] = 0
if len(sas) != 3:
	print(-1)
else:
	nbs = []
	for i in sas:
		nbs.append(set(i))
	a = nbs[0].intersection(nbs[1])
	b = nbs[0].intersection(nbs[2])
	c = nbs[1].intersection(nbs[2])
	kol = [0]*(v+1)
	for i in a:
		kol[i] = 1
	for i in b:
		kol[i] = 2
	for i in c:
		kol[i] = 3
	zer = 0
	for i in range(1,len(kol)):
		if kol[i] == 0:
			zer += 1
			break
	if zer > 0:
		print(-1)
	else:
		if len(a)+len(b)+len(c) !=v:
			print(-1)
		else:
			print(*kol[1:])