시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 512 MB5841139725.594%

문제

N명의 변호사가 사기 범죄를 저지른 혐의로 기소되었다. N명의 변호사는 서로를 변호하여 전원 무사히 무죄로 처리되려고 한다.

변호사들은 자신이 신뢰하는 변호사에게만 변호를 받을 수 있다. 이 신뢰관계란 M개의 (A, B)쌍으로 표현되는데, 이는 변호사 B가 변호사 A를 신뢰한다는 의미로 이 경우에만 변호사 A가 변호사 B를 변호할 수 있다.

각각의 변호사들의 실력은 매우 뛰어나기 때문에, 1명 이상의 변호를 받은 사람은 무조건 무죄가 된다. 단, 두 변호사 A, B에 대해 AB를 변호하고, BA를 변호하는 경우는 매우 수상하기 때문에 둘 모두 유죄가 된다.

각 (A, B) 쌍에 대해 변호사 A가 변호사 B를 변호할지 말지를 선택하여 모든 변호사가 무죄가 되는 것이 가능한지 판정하라.

입력

첫 줄에 NM이 주어진다. (1 ≤ N, M ≤ 200,000)

두 번째 줄부터 줄에 걸쳐 i번째 줄에는 서로 다른 두 정수 Ai, Bi가 주어진다. 이는 변호사 Ai가 변호사 Bi를 변호할 수 있다는 뜻이다.

주어지는 입력에서 순서쌍 (A, B)가 중복하여 나타나는 경우는 없다.

출력

모든 변호사가 1명 이상의 변호를 받고, 서로를 변호하는 변호사 쌍이 없도록 할 수 있는 경우 첫 줄에 YES을 출력한다.

불가능한 경우 첫 줄에 NO를 출력한다.

예제 입력 1

3 3
1 2
2 3
3 1

예제 출력 1

YES

예제 입력 2

4 6
1 2
1 3
1 4
2 3
2 4
3 4

예제 출력 2

NO

예제 입력 3

4 4
1 2
2 1
3 4
4 3

예제 출력 3

NO
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