D. Complete Tripartitetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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:  There are no edges with both endpoints in vertex set v_1.  There are no edges with both endpoints in vertex set v_2.  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;  All vertex sets should not be empty.  Each vertex should be assigned to only one vertex set.  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.InputThe first line contains two integers n and m (3 \le n \le 10^{5}, 0 \le m \le \text{min}(3 \cdot 10^{5}, \frac{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 \le a_{i} \lt b_{i} \le 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.OutputIf 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.ExamplesInput
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
NoteIn 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.  In the second example, it's impossible to make such vertex sets.
6 11
1 2
1 3
1 4
1 5
1 6
2 4
2 5
2 6
3 4
3 5
3 6

1 2 2 3 3 3 
['brute force', 'constructive algorithms', 'graphs', 'hashing', 'implementation', '*1900']