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Michelle's Evaluation
 Time Limit: 5000MS Memory Limit: 131072K Total Submissions: 1632 Accepted: 115

Description

After years of toil designing and evaluating varieties of complex networks, Michelle, an elite engineer, has recently made the decision to develop an assistant software to help herself out.

Consider a network built up with undirected water supply pipes each connecting a pair of junctions that supply or consume water. A shortcut of length L is defined as a sequence of  L distinct junctions such that two junctions are adjacent in the network if and only if they are adjacent in the sequence. A network is regarded speedy if there is no shortcut with a length greater than three.

Now, please try to work out an efficient solution for Michelle to determine whether a network is speedy or not.

Input

The input contains exactly one test case given as specified below:

 Line 1 Two integers N (1 < N < 1,200) and M, which are the numbers of junctions and pipes, respectively. Line 2 – M + 1 Two integer A and B (1 ≤ A, B ≤ N) on each line, describing a pipe connecting junctions A and B.

You can assume that there exists a path between any two junctions.

Output

Output “`Yes`” if the network is speedy, otherwise print “`No`”.

Sample Input

```4 4
1 2
2 3
3 4
4 1```

Sample Output

`Yes`

Source

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