Complete Tripartite

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.

In the second example, it's impossible to make such vertex sets.

inputFormat

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.

outputFormat

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.

In the second example, it's impossible to make such vertex sets.

样例

4 6
1 2
1 3
1 4
2 3
2 4
3 4

-1

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