During a test, Professor Floyd noticed that some of the students were exchanging notes. At first, he wanted to give them all twos, but that day the professor was kind, and therefore he decided to divide the students into two groups: those who cheated and those who let them cheat, and give only the first two.
The professor has a record of all pairs of students who exchanged notes. It is required to determine whether he can divide the students into two groups so that any exchange of notes is carried out from a student of one group to a student of another group.
Input: The first line contains two numbers N and M - the number of students and the number of pairs of students exchanging notes (1<=N<=100, 0<=M<=(N(N−1))/2. Next, M lines contain descriptions of pairs of students: two numbers corresponding to the numbers of students exchanging notes (students are numbered starting from 1) Each pair of students is listed at most one times.
Output: You need to output the answer to Professor Floyd's problem. If it is possible to divide the students into two groups, print YES; otherwise print NO.
Examples
| # |
Input |
Output |
| 1 |
3 2
1 2
2 3
|
YES |
| 2 |
3 3
1 2
2 3
1 3
|
NO |