문제
NLCS Jeju의 학생들은 수업에 질려 학교에서 탈출하고 싶어한다. 수업 시간에 학교에서 탈출하는 것은 어려운 일이다.
NLCS Jeju의 수업 시간은 1ドル$교시부터 $M$교시이다. 또한 NLCS Jeju에 있는 $N$명의 선생님들은 각각 1ドル$교시부터 $M$교시 사이에 정해진 스케줄에 따라 해당 수업 시간 동안 순찰한다. 학교에서 탈출하다 선생님에게 들키면 안 되기 때문에 학생들은 아무도 순찰하지 않을 때 학교에서 탈출해야 한다. 학교 탈출을 시도하려는 시각에 순찰하는 선생님이 있다면 선생님에게 무조건 들킨다.
각 선생님의 순찰 스케줄이 주어질 때 학생들이 학교에서 탈출할 수 있는지 판단하고, 가능하다면 학교에서 탈출할 수 있는 가장 빠른 시각을 구하자.
출력
학생들이 선생님에게 들키지 않고 가장 빠르게 학교에서 탈출했을 때가 몇 교시인지 출력하라. 학생들이 선생님에게 들키지 않고 학교에서 탈출할 수 없다면 ESCAPE FAILED를 출력하라.
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