Non-Punishable Road Connectivity

You are given n intersections and m potential roads. Each road connects two intersections u and v. However, due to regulations only roads connecting intersections of different types (i.e. one with an odd number and one with an even number) are non-punishable and can be used. In other words, a road is valid if and only if

\( u \bmod 2 \neq v \bmod 2 \)

Your task is to determine if it is possible to use these non-punishable roads to connect all intersections. The intersections are numbered from 1 to n.

If all intersections can be connected using only valid roads, print YES; otherwise, print NO.

inputFormat

The first line contains two space-separated integers, n and m, where n is the number of intersections and m is the number of potential roads. Each of the next m lines contains two space-separated integers u and v, representing a road between intersections u and v.

outputFormat

Output a single line with the answer: YES if all intersections can be connected using only non-punishable roads, or NO otherwise.

4 4
1 2
2 3
3 4
4 1

YES