34088번
- It's a Mod, Mod, Mod, Mod World 2
다국어
문제
서로 다른 양의 정수 $N$개로 이루어진 집합 $A$가 주어진다. $A$의 부분집합과 1ドル$보다 큰 정수 $K$를 적절히 골라, 부분집합의 모든 원소를 $K$로 나눈 나머지가 서로 같게 하려고 한다.
고를 수 있는 부분집합의 최대 크기를 구하여라.
출력
고를 수 있는 부분집합의 최대 크기를 출력한다.
$A$의 부분집합 $\{5,8,11\},ドル $K = 3$을 골라 크기 3ドル$의 부분집합을 고를 수 있다.
크기 4ドル$ 이상의 부분집합을 고를 수 없으므로, 고를 수 있는 부분집합의 최대 크기는 3ドル$이다.
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