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## Четвертьфинал, Рыбинск, 16 октября 2003

Соревнование завершено

## G. Topological Sorting

Ограничение времени: 1.0 секунды
Ограничение памяти: 64 МБ
Michael wants to win the world championship in programming and decided to study N subjects (for convenience we will number these subjects from 1 to N). Michael has worked out a study plan for this purpose. But it turned out that certain subjects may be studied only after others. So, Michael’s coach analyzed all subjects and prepared a list of M limitations in the form “si ui(1 ≤ si, uiN; i = 1, 2, …, M), which means that subject si must be studied before subject ui.
Your task is to verify if the order of subjects being studied is correct.
Remark. It may appear that it’s impossible to find the correct order of subjects within the given limitations. In this case any subject order worked out by Michael is incorrect.
Limitations
1 ≤ N ≤ 1000; 0 ≤ M ≤ 100000.

### Исходные данные

The first line contains two integers N and M (N is the number of the subjects, M is the number of the limitations). The next M lines contain pairs si, ui, which describe the order of subjects: subject si must be studied before ui. Further there is a sequence of N unique numbers ranging from 1 to N — the proposed study plan.

### Результат

Output a single word “YES” or “NO”. “YES” means that the proposed order is correct and has no contradictions with the given limitations. “NO” means that the order is incorrect.

### Примеры

исходные данныерезультат
```5 6
1 3
1 4
3 5
5 2
4 2
1 2
1 3 4 5 2
```
```YES
```
```5 6
1 3
1 4
3 5
5 2
4 2
1 2
1 2 4 5 3
```
```NO
```
Автор задачи: © Sergey G. Volchenkov, 2003(volchenkov@yandex.ru); Vladimir N. Pinaev, 2003(vpinaev@mail.ru; http://www.pic200x.chat.ru); Michael Y. Kopachev, 2003 (mkopachev@krista.ru).
Источник задачи: 2003-2004 ACM Central Region of Russia Quarterfinal Programming Contest, Rybinsk, October 15-16, 2003
Чтобы отправить решение этой задачи на проверку перейдите в Архив задач: 1280. Topological Sorting