Non-Consecutive Vertex Labeling

You are given an undirected graph with n vertices and m edges. Your task is to assign a permutation of numbers from 1 to n to the vertices such that for every edge connecting vertices u and v, the absolute difference between the numbers assigned to u and v is not equal to 1.

If such a labeling exists, print YES on the first line and one valid labeling (the numbers assigned to vertices 1,2,...,n in order) on the second line. Otherwise, print NO.

The problem can be formally stated as follows. Let \(f: \{1, 2, \dots, n\} \to \{1, 2, \dots, n\}\) be a permutation. For every edge \((u, v)\), it must hold that:

[ |f(u) - f(v)| \neq 1. ]

It is guaranteed that the input size is small so that a backtracking solution exploring all permutations is acceptable.

inputFormat

The first line of input contains two integers n and m separated by a space, where n is the number of vertices and m is the number of edges.

The following m lines each contain two integers u and v (1-based indices) representing an edge between vertices u and v.

outputFormat

If a valid labeling exists, output YES on the first line, and on the second line output n integers—the labeling for vertices 1 through n—separated by spaces. If no valid labeling exists, output only NO.

## sample

4 3
1 2
2 3
3 4

YES
2 4 1 3

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