시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 32 14 14 50.000%

문제

상근이와 정인이는 숫자 맞추기 게임을 하고 있다.

먼저, 정인이는 1보다 크거나 같고, n보다 작거나 같은 자연수 하나를 생각한다.

상근이는 정인이에게 생각한 숫자가 x인지 물어볼 수 있다. 이때 정인이는 자신이 생각한 숫자와 x의 최대공약수가 몇 인지 말해준다.

다음은 n=6일 때 가능한 상근이와 정인이의 대화이다.

상근: 3이야?

정인: 3이랑 내가 생각한 숫자의 최대공약수는 1이야.

상근: (음... 그럼 3이랑 6은 아니네? 근데 1,2,4,5는 될 수 있어!) 그럼 2야?

정인: 2랑 내가 생각한 숫자의 최대공약수는 2야.

상근: (오!? 그럼 1, 5는 아니겠네?) 너가 생각한 숫자는 4야 맞지?

정인: 4랑 내가 생각한 숫자의 최대공약수는 2야.

상근: 그럼 니가 생각한 숫자는 2네 ㅋㅋㅋ

위의 예에서 상근이는 정인이가 생각한 숫자를 맞추기 위해서 질문을 총 3번 했다. 하지만, n=6인 경우에 항상 2번의 질문으로 정인이가 생각한 숫자를 맞출 수 있다.

제일 먼저 상근이는 6을 물어보면 된다. 만약 정인이가 1이라고 대답했다면, 정인이가 생각한 숫자는 1과 5중 하나이기 때문에, 2번 질문으로 맞출 수 있다. 정인이의 대답이 2라면, 정인이가 생각한 숫자는 2와 4중 하나이다. 만약, 정인이가 3이라고 대답했다면, 정답은 3이고, 6이라고 대답했다면 6이다.

따라서, 상근이는 최대 2번의 질문으로 정인이가 생각한 숫자를 맞출 수 있다.

n이 주어졌을 때, 상근이가 최적의 방법으로 질문했을 때, 최대 몇 번 만에 정인이가 생각한 숫자를 맞출 수 있는지 구하는 프로그램을 작성하시오.

입력

첫째 줄에 n이 주어진다. 2 ≤ n ≤ 10,000

출력

첫째 줄에 상근이가 최적의 방법으로 질문했을 때, 최대 몇 번의 질문으로 정인이가 생각한 숫자를 맞출 수 있는지 출력한다.

예제 입력 1

6

예제 출력 1

2
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Andrew knew that Paul&rsquo;s age is an integer between 1 and n, inclusive. Andrew can guess any number x between 1 and n, and Paul will tell him what is the greatest common divisor of x and his age.<\/p>\r\n\r\n<p>Here&rsquo;s a possible course of the game for n = 6. Andrew starts with guessing 3, and Paul replies that the greatest common divisor of 3 and his age is 1. That means that Paul&rsquo;s age can&rsquo;t be 3 or 6, but can still be 1, 2, 4 or 5. Andrew continues with guessing 2, and Paul replies 2. That means that Paul&rsquo;s age can&rsquo;t be 1 or 5, and the only two remaining choices are 2 and 4. Finally, Andrew guesses 4, and Paul replies 2. That means that Paul&rsquo;s age is 2, and the game is over.<\/p>\r\n\r\n<p>Andrew needed three guesses in the above example, but it&rsquo;s possible to always determine Paul&rsquo;s age in at most two guesses for n = 6. The optimal strategy for Andrew is: at the \ufb01rst step, guess 6. If Paul says 1, then its 1 or 5 and he can check which one by guessing 5. If Paul says 2, then its 2 or 4, and he can check by guesing 4 as we&rsquo;ve seen above. If Paul says 3, then we already know the answer is 3. Finally, if Paul says 6, the answer is 6.<\/p>\r\n\r\n<p>What is the number of guesses required in the worst case if Andrew guesses optimally for the given n?<\/p>\r\n","input":"<p>The input \ufb01le contains one integer n, 2 &le; n &le; 10 000.<\/p>\r\n","output":"<p>Output one integer &mdash; the number of guesses Andrew will need to make in the worst case.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]