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:

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

Output

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

4 4
1 2
2 3
3 4
4 1

Yes

Source

POJ Monthly--2007.06.03, Jia, You