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.
import sys
input = sys.stdin.readline
import collections

def tripartite(n, edges):
    graph = {}
    for i in range(n): graph[i] = set()
    for e1, e2 in edges:
        graph[e1].add(e2)
        graph[e2].add(e1)

    visited = [False] * n
    q = collections.deque()
    q.append(0)
    while q:
        lenq = len(q)
        for _ in range(lenq):
            cur = q.popleft()
            if visited[cur]: continue
            visited[cur] = True
            for nei in graph[cur]: q.append(nei)

    if not all(visited): return [-1] # graph is not single connected

    colors = [0] * n
    q = collections.deque()
    color = 1
    for i in range(n):
        if colors[i] != 0: continue
        q.append(i)
        while q:
            lenq = len(q)
            for _ in range(lenq):
                cur = q.popleft()
                if colors[cur] != 0: continue
                colors[cur] = color
                for nei in graph[cur]: q.append(nei)
            color = 3 - color
    #print(colors)
    for i in range(n):
        if colors[i] != 1: colors[i] = 0
    #print(colors)
    for i in range(n):
        if colors[i] != 0: continue
        q.append(i)
        color = 2
        while q:
            lenq = len(q)
            for _ in range(lenq):
                cur = q.popleft()
                if colors[cur] != 0:
                    if colors[cur] == 1: continue
                    if colors[cur] == color: continue # visited node
                    if colors[cur] != color: return [-1] # visited node with contradiction
                colors[cur] = color
                for nei in graph[cur]: q.append(nei)
            #print(colors)
            color = 5 - color

    if len(set(colors)) < 3: return [-1]

    counter = collections.Counter(colors)
    for i in range(n):
        if len(graph[i]) < n - counter[colors[i]]: return [-1]

    for i in range(n):
        for nei in graph[i]:
            if colors[i] == colors[nei]: return [-1]

    return colors

def main():
    n, m = input().split()
    n, m = int(n), int(m)
    edges = []
    for _ in range(m):
        e1, e2 = input().split()
        edges.append((int(e1) - 1, int(e2) - 1))
    print(' '.join(map(str, tripartite(n, edges))))

if __name__ == '__main__':
    main()