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문제

블랑콘씨의 집 주위를 돌아다니는 $N$ 마리의 곤충이 있고, 각각 $0$에서 $N - 1$로 번호가 매겨져 있다. 각 곤충마다 자신이 속하는 종류가 있고, $0$ 이상 $10^9$ 이하인 정수로 표현된다. 복수의 곤충이 같은 종류에 속할 수 있다.

곤충들을 종류에 따라 그룹으로 모아보기로 하자. 가장 자주 나오는 곤충 종류 그룹의 크기는 가장 많은 수의 곤충이 속하는 그룹의 곤충 수이다. 비슷하게, 가장 드문 곤충 종류 그룹의 크기는 가장 적은 수의 곤충이 속하는 그룹의 곤충 수이다.

예를 들어, $11$ 마리의 곤충이 있고, 종류가 차례로 $[5, 7, 9, 11, 11, 5, 0, 11, 9, 100, 9]$라고 하자. 이 경우, 가장 자주 나오는 곤충 종류 그룹의 크기는 $3$이다. 종류 $9$인 곤충의 그룹과 종류 $11$인 곤충의 그룹이 가장 자주 나오는 곤충 종류 그룹이며, 각각 $3$ 마리의 곤충으로 이루어져 있다. 가장 드문 곤충 종류 그룹의 크기는 $1$이다. 종류 $7$, 종류 $0$, 종류 $100$인 곤충의 그룹에는 각각 $1$ 마리의 곤충이 속한다.

블랑콘씨는 곤충의 종류를 알지 못한다. 곤충의 종류에 대한 정보를 알려주는 단추가 하나 달린 기계가 있다. 처음, 이 기계는 비어 있다. 기계를 이용하기 위해, 다음 세 가지 종류의 연산을 사용할 수 있다.

  1. 곤충 한 마리를 기계 안에 넣는다.
  2. 곤충 한 마리를 기계에서 빼낸다.
  3. 기계의 단추를 누른다.

각각의 연산은 최대 $40\,000$ 번 수행될 수 있다.

단추가 눌려질 때마다, 이 기계는 현재 기계에 들어 있는 곤충들만 이용해서, 이 중 가장 자주 나오는 곤충 종류 그룹의 크기를 알려준다.

당신이 할 일은 이 기계를 사용해서 블랑콘씨 집 주위의 $N$ 마리 곤충들 중 가장 드문 곤충 종류 그룹의 크기를 구하는 것이다. 덤으로, 어떤 서브태스크에서는, 특정한 명령이 실행되는 횟수에 따라 여러분의 점수가 결정된다 (자세한 내용은 Subtasks 참고).

구현

다음 함수를 구현해야 한다.

int min_cardinality(int N)
  • $N$: 곤충의 수
  • 이 함수는 블랑콘씨 집 주위에 있는 모든 $N$ 마리 곤충들 중 가장 드문 곤충 종류 그룹의 크기를 리턴해야 한다.
  • 이 함수는 정확히 한 번 호출된다.

위 함수는 다음 함수들을 호출할 수 있다.

void move_inside(int i)
  • $i$: 기계에 집어넣을 곤충의 인덱스. $i$ 값은 $0$ 이상 $N - 1$ 이하여야 한다.
  • 만약 이 곤충이 이미 기계 안에 있다면, 이 함수 호출은 기계 안에 있는 곤충의 집합을 바꾸지 않는다. 하지만 이 호출도 별도의 함수 호출 한 번으로 계산된다.
  • 이 함수는 최대 $40\,000$ 번 호출될 수 있다.
void move_outside(int i)
  • $i$: 기계에서 뺄 곤충의 인덱스. $i$ 값은 $0$ 이상 $N - 1$ 이하여야 한다.
  • 만약 이 곤충이 이미 기계 밖에 있다면, 이 함수 호출은 기계 안에 있는 곤충의 집합을 바꾸지 않는다. 하지만 이 호출도 별도의 함수 호출 한 번으로 계산된다.
  • 이 함수는 최대 $40\,000$ 번 호출될 수 있다.
int press_button()
  • 이 함수는 기계 안에 있는 곤충들 중에서, 가장 자주 나오는 곤충 종류 그룹의 크기를 알려준다. 전체 곤충이 아니고 기계 안에 있는 곤충만 고려한다는데 유의하라.
  • 이 함수는 최대 $40\,000$ 번 호출될 수 있다.
  • 그레이더는 적응적(adaptive)이지 않다. 즉, 곤충 $N$ 마리의 종류는 min_cardinality 함수를 호출하기 전에 이미 결정되어 있다.

예제

$6$ 마리 곤충이 있고, 종류가 차례로 $[5, 8, 9, 5, 9, 9]$인 시나리오를 생각해보자. min_cardinality 함수는 다음과 같이 호출된다.

min_cardinality(6)

이 함수는 move_inside, move_outside, press_button를 다음과 같이 호출한다.

호출하는 함수 리턴 값 기계 안에 있는 곤충 기계 안의 곤충들 종류
$\{\}$ $[]$
move_inside(0) $\{0\}$ $[5]$
press_button() $1$ $\{0\}$ $[5]$
move_inside(1) $\{0, 1\}$ $[5, 8]$
press_button() $1$ $\{0, 1\}$ $[5, 8]$
move_inside(3) $\{0, 1, 3\}$ $[5, 8, 5]$
press_button() $2$ $\{0, 1, 3\}$ $[5, 8, 5]$
move_inside(2) $\{0, 1, 2, 3\}$ $[5, 8, 9, 5]$
move_inside(4) $\{0, 1, 2, 3, 4\}$ $[5, 8, 9, 5, 9]$
move_inside(5) $\{0, 1, 2, 3, 4, 5\}$ $[5, 8, 9, 5, 9, 9]$
press_button() $3$ $\{0, 1, 2, 3, 4, 5\}$ $[5, 8, 9, 5, 9, 9]$
move_inside(5) $\{0, 1, 2, 3, 4, 5\}$ $[5, 8, 9, 5, 9, 9]$
press_button() $3$ $\{0, 1, 2, 3, 4, 5\}$ $[5, 8, 9, 5, 9, 9]$
move_outside(5) $\{0, 1, 2, 3, 4\}$ $[5, 8, 9, 5, 9]$
press_button() $2$ $\{0, 1, 2, 3, 4\}$ $[5, 8, 9, 5, 9]$

이 시점에서, 가장 드문 곤충 종류 그룹의 크기가 $1$ 임을 아는데 충분한 정보를 얻게 된다. 따라서, min_cardinality 함수의 리턴값은 $1$이어야 한다.

이 예제에서, move_inside 함수는 $7$ 번, move_outside 함수는 $1$ 번, press_button 함수는 $6$ 번 호출되었다.

제한

  • $2 \le N \le 2000$

서브태스크

번호배점제한
110

$N \le 200$

215

$N \le 1000$

375

추가적인 제약 조건이 없다.

어떤 테스트 케이스에서든, 함수 move_inside, move_outside, press_button를 호출할 때 Implementation Details에서 설명한 제약 조건을 만족하지 않았다거나, min_cardinality 함수의 출력이 틀렸다면, 해당 서브태스크에서 여러분의 점수는 $0$점이다.

$q$가 move_inside 함수 호출 횟수, move_outside 함수 호출 횟수, press_button 함수 호출 횟수 세 값 중 최대값이라고 하자.

서브태스크 3에서는 부분 점수가 있다. $m$이 이 서브태스크의 모든 테스트케이스에서 $\frac{q}{N}$의 최대값이라고 하자. 이 서브태스크에서 얻을 수 있는 점수는 다음 표에 따라 계산된다.

조건 점수
$20 \lt m$ $0$ (CMS에서 "Output isn’t correct"로 출력)
$6 \lt m \le 20$ $\frac{225}{m - 2}$
$3 \lt m \le 6$ $81 - \frac{2}{3} m^2$
$m \le 3$ $75$
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\uadf8\ub8f9\uc758 \uace4\ucda9 \uc218\uc774\ub2e4. \ube44\uc2b7\ud558\uac8c, <strong>\uac00\uc7a5 \ub4dc\ubb38<\/strong> \uace4\ucda9 \uc885\ub958 \uadf8\ub8f9\uc758 \ud06c\uae30\ub294 \uac00\uc7a5 \uc801\uc740 \uc218\uc758 \uace4\ucda9\uc774 \uc18d\ud558\ub294 \uadf8\ub8f9\uc758 \uace4\ucda9 \uc218\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, $11$ \ub9c8\ub9ac\uc758 \uace4\ucda9\uc774 \uc788\uace0, \uc885\ub958\uac00 \ucc28\ub840\ub85c $[5, 7, 9, 11, 11, 5, 0, 11, 9, 100, 9]$\ub77c\uace0 \ud558\uc790. \uc774 \uacbd\uc6b0, <strong>\uac00\uc7a5 \uc790\uc8fc \ub098\uc624\ub294<\/strong> \uace4\ucda9 \uc885\ub958 \uadf8\ub8f9\uc758 \ud06c\uae30\ub294 $3$\uc774\ub2e4. \uc885\ub958 $9$\uc778 \uace4\ucda9\uc758 \uadf8\ub8f9\uacfc \uc885\ub958 $11$\uc778 \uace4\ucda9\uc758 \uadf8\ub8f9\uc774 \uac00\uc7a5 \uc790\uc8fc \ub098\uc624\ub294 \uace4\ucda9 \uc885\ub958 \uadf8\ub8f9\uc774\uba70, \uac01\uac01 $3$ \ub9c8\ub9ac\uc758 \uace4\ucda9\uc73c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. <strong>\uac00\uc7a5 \ub4dc\ubb38<\/strong> \uace4\ucda9 \uc885\ub958 \uadf8\ub8f9\uc758 \ud06c\uae30\ub294 $1$\uc774\ub2e4. \uc885\ub958 $7$, \uc885\ub958 $0$, \uc885\ub958 $100$\uc778 \uace4\ucda9\uc758 \uadf8\ub8f9\uc5d0\ub294 \uac01\uac01 $1$ \ub9c8\ub9ac\uc758 \uace4\ucda9\uc774 \uc18d\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ube14\ub791\ucf58\uc528\ub294 \uace4\ucda9\uc758 \uc885\ub958\ub97c \uc54c\uc9c0 \ubabb\ud55c\ub2e4. \uace4\ucda9\uc758 \uc885\ub958\uc5d0 \ub300\ud55c \uc815\ubcf4\ub97c \uc54c\ub824\uc8fc\ub294 \ub2e8\ucd94\uac00 \ud558\ub098 \ub2ec\ub9b0 \uae30\uacc4\uac00 \uc788\ub2e4. \ucc98\uc74c, \uc774 \uae30\uacc4\ub294 \ube44\uc5b4 \uc788\ub2e4. \uae30\uacc4\ub97c \uc774\uc6a9\ud558\uae30 \uc704\ud574, \ub2e4\uc74c \uc138 \uac00\uc9c0 \uc885\ub958\uc758 \uc5f0\uc0b0\uc744 \uc0ac\uc6a9\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<ol>\r\n\t<li>\uace4\ucda9 \ud55c \ub9c8\ub9ac\ub97c \uae30\uacc4 \uc548\uc5d0 \ub123\ub294\ub2e4.<\/li>\r\n\t<li>\uace4\ucda9 \ud55c \ub9c8\ub9ac\ub97c \uae30\uacc4\uc5d0\uc11c \ube7c\ub0b8\ub2e4.<\/li>\r\n\t<li>\uae30\uacc4\uc758 \ub2e8\ucd94\ub97c \ub204\ub978\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p>\uac01\uac01\uc758 \uc5f0\uc0b0\uc740 \ucd5c\ub300 $40\\,000$ \ubc88 \uc218\ud589\ub420 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ub2e8\ucd94\uac00 \ub20c\ub824\uc9c8 \ub54c\ub9c8\ub2e4, \uc774 \uae30\uacc4\ub294 \ud604\uc7ac \uae30\uacc4\uc5d0 \ub4e4\uc5b4 \uc788\ub294 \uace4\ucda9\ub4e4\ub9cc \uc774\uc6a9\ud574\uc11c, \uc774 \uc911 <strong>\uac00\uc7a5 \uc790\uc8fc \ub098\uc624\ub294<\/strong> \uace4\ucda9 \uc885\ub958 \uadf8\ub8f9\uc758 \ud06c\uae30\ub97c \uc54c\ub824\uc900\ub2e4.<\/p>\r\n\r\n<p>\ub2f9\uc2e0\uc774 \ud560 \uc77c\uc740 \uc774 \uae30\uacc4\ub97c \uc0ac\uc6a9\ud574\uc11c \ube14\ub791\ucf58\uc528 \uc9d1 \uc8fc\uc704\uc758 $N$ \ub9c8\ub9ac \uace4\ucda9\ub4e4 \uc911 <strong>\uac00\uc7a5 \ub4dc\ubb38<\/strong> \uace4\ucda9 \uc885\ub958 \uadf8\ub8f9\uc758 \ud06c\uae30\ub97c \uad6c\ud558\ub294 \uac83\uc774\ub2e4. \ub364\uc73c\ub85c, \uc5b4\ub5a4 \uc11c\ube0c\ud0dc\uc2a4\ud06c\uc5d0\uc11c\ub294, \ud2b9\uc815\ud55c \uba85\ub839\uc774 \uc2e4\ud589\ub418\ub294 \ud69f\uc218\uc5d0 \ub530\ub77c \uc5ec\ub7ec\ubd84\uc758 \uc810\uc218\uac00 \uacb0\uc815\ub41c\ub2e4 (\uc790\uc138\ud55c \ub0b4\uc6a9\uc740 Subtasks \ucc38\uace0).<\/p>\r\n","input":"","output":"","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>$2 \\le N \\le 2000$<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$N \\le 200$<\/p>\r\n","subtask2":"<p>$N \\le 1000$<\/p>\r\n","subtask3":"<p>\ucd94\uac00\uc801\uc778 \uc81c\uc57d \uc870\uac74\uc774 \uc5c6\ub2e4.<\/p>\r\n","custom_implementation":"<p>\ub2e4\uc74c \ud568\uc218\ub97c \uad6c\ud604\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<pre>\r\n<code>int min_cardinality(int N)\r\n<\/code><\/pre>\r\n\r\n<ul>\r\n\t<li>$N$: \uace4\ucda9\uc758 \uc218<\/li>\r\n\t<li>\uc774 \ud568\uc218\ub294 \ube14\ub791\ucf58\uc528 \uc9d1 \uc8fc\uc704\uc5d0 \uc788\ub294 \ubaa8\ub4e0 $N$ \ub9c8\ub9ac \uace4\ucda9\ub4e4 \uc911 <strong>\uac00\uc7a5 \ub4dc\ubb38<\/strong> \uace4\ucda9 \uc885\ub958 \uadf8\ub8f9\uc758 \ud06c\uae30\ub97c \ub9ac\ud134\ud574\uc57c \ud55c\ub2e4.<\/li>\r\n\t<li>\uc774 \ud568\uc218\ub294 \uc815\ud655\ud788 \ud55c \ubc88 \ud638\ucd9c\ub41c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc704 \ud568\uc218\ub294 \ub2e4\uc74c \ud568\uc218\ub4e4\uc744 \ud638\ucd9c\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<pre>\r\n<code>void move_inside(int i)\r\n<\/code><\/pre>\r\n\r\n<ul>\r\n\t<li>$i$: \uae30\uacc4\uc5d0 \uc9d1\uc5b4\ub123\uc744 \uace4\ucda9\uc758 \uc778\ub371\uc2a4. $i$ \uac12\uc740 $0$ \uc774\uc0c1 $N - 1$ \uc774\ud558\uc5ec\uc57c \ud55c\ub2e4.<\/li>\r\n\t<li>\ub9cc\uc57d \uc774 \uace4\ucda9\uc774 \uc774\ubbf8 \uae30\uacc4 \uc548\uc5d0 \uc788\ub2e4\uba74, \uc774 \ud568\uc218 \ud638\ucd9c\uc740 \uae30\uacc4 \uc548\uc5d0 \uc788\ub294 \uace4\ucda9\uc758 \uc9d1\ud569\uc744 \ubc14\uafb8\uc9c0 \uc54a\ub294\ub2e4. \ud558\uc9c0\ub9cc \uc774 \ud638\ucd9c\ub3c4 \ubcc4\ub3c4\uc758 \ud568\uc218 \ud638\ucd9c \ud55c \ubc88\uc73c\ub85c \uacc4\uc0b0\ub41c\ub2e4.<\/li>\r\n\t<li>\uc774 \ud568\uc218\ub294 \ucd5c\ub300 $40\\,000$ \ubc88 \ud638\ucd9c\ub420 \uc218 \uc788\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<pre>\r\n<code>void move_outside(int i)\r\n<\/code><\/pre>\r\n\r\n<ul>\r\n\t<li>$i$: \uae30\uacc4\uc5d0\uc11c \ube84 \uace4\ucda9\uc758 \uc778\ub371\uc2a4. $i$ \uac12\uc740 $0$ \uc774\uc0c1 $N - 1$ \uc774\ud558\uc5ec\uc57c \ud55c\ub2e4.<\/li>\r\n\t<li>\ub9cc\uc57d \uc774 \uace4\ucda9\uc774 \uc774\ubbf8 \uae30\uacc4 \ubc16\uc5d0 \uc788\ub2e4\uba74, \uc774 \ud568\uc218 \ud638\ucd9c\uc740 \uae30\uacc4 \uc548\uc5d0 \uc788\ub294 \uace4\ucda9\uc758 \uc9d1\ud569\uc744 \ubc14\uafb8\uc9c0 \uc54a\ub294\ub2e4. \ud558\uc9c0\ub9cc \uc774 \ud638\ucd9c\ub3c4 \ubcc4\ub3c4\uc758 \ud568\uc218 \ud638\ucd9c \ud55c \ubc88\uc73c\ub85c \uacc4\uc0b0\ub41c\ub2e4.<\/li>\r\n\t<li>\uc774 \ud568\uc218\ub294 \ucd5c\ub300 $40\\,000$ \ubc88 \ud638\ucd9c\ub420 \uc218 \uc788\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<pre>\r\n<code>int press_button()\r\n<\/code><\/pre>\r\n\r\n<ul>\r\n\t<li>\uc774 \ud568\uc218\ub294 \uae30\uacc4 \uc548\uc5d0 \uc788\ub294 \uace4\ucda9\ub4e4 \uc911\uc5d0\uc11c, <strong>\uac00\uc7a5 \uc790\uc8fc \ub098\uc624\ub294<\/strong> \uace4\ucda9 \uc885\ub958 \uadf8\ub8f9\uc758 \ud06c\uae30\ub97c \uc54c\ub824\uc900\ub2e4. \uc804\uccb4 \uace4\ucda9\uc774 \uc544\ub2c8\uace0 \uae30\uacc4 \uc548\uc5d0 \uc788\ub294 \uace4\ucda9\ub9cc \uace0\ub824\ud55c\ub2e4\ub294\ub370 \uc720\uc758\ud558\ub77c.<\/li>\r\n\t<li>\uc774 \ud568\uc218\ub294 \ucd5c\ub300 $40\\,000$ \ubc88 \ud638\ucd9c\ub420 \uc218 \uc788\ub2e4.<\/li>\r\n\t<li>\uadf8\ub808\uc774\ub354\ub294 <strong>\uc801\uc751\uc801(adaptive)\uc774\uc9c0 \uc54a\ub2e4.<\/strong> \uc989, \uace4\ucda9 $N$ \ub9c8\ub9ac\uc758 \uc885\ub958\ub294 <code>min_cardinality<\/code> \ud568\uc218\ub97c \ud638\ucd9c\ud558\uae30 \uc804\uc5d0 \uc774\ubbf8 \uacb0\uc815\ub418\uc5b4 \uc788\ub2e4.<\/li>\r\n<\/ul>\r\n","custom_example":"<p>$6$ \ub9c8\ub9ac \uace4\ucda9\uc774 \uc788\uace0, \uc885\ub958\uac00 \ucc28\ub840\ub85c $[5, 8, 9, 5, 9, 9]$\uc778 \uc2dc\ub098\ub9ac\uc624\ub97c \uc0dd\uac01\ud574\ubcf4\uc790. <code>min_cardinality<\/code> \ud568\uc218\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \ud638\ucd9c\ub41c\ub2e4.<\/p>\r\n\r\n<pre>\r\n<code>min_cardinality(6)\r\n<\/code><\/pre>\r\n\r\n<p>\uc774 \ud568\uc218\ub294 <code>move_inside<\/code>, <code>move_outside<\/code>, <code>press_button<\/code>\ub97c \ub2e4\uc74c\uacfc \uac19\uc774 \ud638\ucd9c\ud55c\ub2e4.<\/p>\r\n\r\n<table class=\"table table-bordered th-center td-center\">\r\n\t<thead>\r\n\t\t<tr>\r\n\t\t\t<th>\ud638\ucd9c\ud558\ub294 \ud568\uc218<\/th>\r\n\t\t\t<th>\ub9ac\ud134 \uac12<\/th>\r\n\t\t\t<th>\uae30\uacc4 \uc548\uc5d0 \uc788\ub294 \uace4\ucda9<\/th>\r\n\t\t\t<th>\uae30\uacc4 \uc548\uc758 \uace4\ucda9\ub4e4 \uc885\ub958<\/th>\r\n\t\t<\/tr>\r\n\t<\/thead>\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td> <\/td>\r\n\t\t\t<td>$\\{\\}$<\/td>\r\n\t\t\t<td>$[]$<\/td>\r\n\t\t\t<td> <\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>move_inside(0)<\/code><\/td>\r\n\t\t\t<td> <\/td>\r\n\t\t\t<td>$\\{0\\}$<\/td>\r\n\t\t\t<td>$[5]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>press_button()<\/code><\/td>\r\n\t\t\t<td>$1$<\/td>\r\n\t\t\t<td>$\\{0\\}$<\/td>\r\n\t\t\t<td>$[5]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>move_inside(1)<\/code><\/td>\r\n\t\t\t<td> <\/td>\r\n\t\t\t<td>$\\{0, 1\\}$<\/td>\r\n\t\t\t<td>$[5, 8]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>press_button()<\/code><\/td>\r\n\t\t\t<td>$1$<\/td>\r\n\t\t\t<td>$\\{0, 1\\}$<\/td>\r\n\t\t\t<td>$[5, 8]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>move_inside(3)<\/code><\/td>\r\n\t\t\t<td> <\/td>\r\n\t\t\t<td>$\\{0, 1, 3\\}$<\/td>\r\n\t\t\t<td>$[5, 8, 5]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>press_button()<\/code><\/td>\r\n\t\t\t<td>$2$<\/td>\r\n\t\t\t<td>$\\{0, 1, 3\\}$<\/td>\r\n\t\t\t<td>$[5, 8, 5]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>move_inside(2)<\/code><\/td>\r\n\t\t\t<td> <\/td>\r\n\t\t\t<td>$\\{0, 1, 2, 3\\}$<\/td>\r\n\t\t\t<td>$[5, 8, 9, 5]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>move_inside(4)<\/code><\/td>\r\n\t\t\t<td> <\/td>\r\n\t\t\t<td>$\\{0, 1, 2, 3, 4\\}$<\/td>\r\n\t\t\t<td>$[5, 8, 9, 5, 9]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>move_inside(5)<\/code><\/td>\r\n\t\t\t<td> <\/td>\r\n\t\t\t<td>$\\{0, 1, 2, 3, 4, 5\\}$<\/td>\r\n\t\t\t<td>$[5, 8, 9, 5, 9, 9]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>press_button()<\/code><\/td>\r\n\t\t\t<td>$3$<\/td>\r\n\t\t\t<td>$\\{0, 1, 2, 3, 4, 5\\}$<\/td>\r\n\t\t\t<td>$[5, 8, 9, 5, 9, 9]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>move_inside(5)<\/code><\/td>\r\n\t\t\t<td> <\/td>\r\n\t\t\t<td>$\\{0, 1, 2, 3, 4, 5\\}$<\/td>\r\n\t\t\t<td>$[5, 8, 9, 5, 9, 9]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>press_button()<\/code><\/td>\r\n\t\t\t<td>$3$<\/td>\r\n\t\t\t<td>$\\{0, 1, 2, 3, 4, 5\\}$<\/td>\r\n\t\t\t<td>$[5, 8, 9, 5, 9, 9]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>move_outside(5)<\/code><\/td>\r\n\t\t\t<td> <\/td>\r\n\t\t\t<td>$\\{0, 1, 2, 3, 4\\}$<\/td>\r\n\t\t\t<td>$[5, 8, 9, 5, 9]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>press_button()<\/code><\/td>\r\n\t\t\t<td>$2$<\/td>\r\n\t\t\t<td>$\\{0, 1, 2, 3, 4\\}$<\/td>\r\n\t\t\t<td>$[5, 8, 9, 5, 9]$<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>\uc774 \uc2dc\uc810\uc5d0\uc11c, \uac00\uc7a5 \ub4dc\ubb38 \uace4\ucda9 \uc885\ub958 \uadf8\ub8f9\uc758 \ud06c\uae30\uac00 $1$ \uc784\uc744 \uc544\ub294\ub370 \ucda9\ubd84\ud55c \uc815\ubcf4\ub97c \uc5bb\uac8c \ub41c\ub2e4. \ub530\ub77c\uc11c, <code>min_cardinality<\/code> \ud568\uc218\uc758 \ub9ac\ud134\uac12\uc740 $1$\uc774\uc5b4\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc774 \uc608\uc81c\uc5d0\uc11c, <code>move_inside<\/code> \ud568\uc218\ub294 $7$ \ubc88, <code>move_outside<\/code> \ud568\uc218\ub294 $1$ \ubc88,  <code>press_button<\/code> \ud568\uc218\ub294 $6$ \ubc88 \ud638\ucd9c\ub418\uc5c8\ub2e4.<\/p>\r\n","custom_subtask_scoring_a":"<p>\uc5b4\ub5a4 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0\uc11c\ub4e0, \ud568\uc218 <code>move_inside<\/code>, <code>move_outside<\/code>, <code>press_button<\/code>\ub97c \ud638\ucd9c\ud560 \ub54c Implementation Details\uc5d0\uc11c \uc124\uba85\ud55c \uc81c\uc57d \uc870\uac74\uc744 \ub9cc\uc871\ud558\uc9c0 \uc54a\uc558\ub2e4\uac70\ub098, <code>min_cardinality<\/code> \ud568\uc218\uc758 \ucd9c\ub825\uc774 \ud2c0\ub838\ub2e4\uba74, \ud574\ub2f9 \uc11c\ube0c\ud0dc\uc2a4\ud06c\uc5d0\uc11c \uc5ec\ub7ec\ubd84\uc758 \uc810\uc218\ub294 $0$\uc810\uc774\ub2e4.<\/p>\r\n\r\n<p>$q$\uac00 <code>move_inside<\/code> \ud568\uc218 \ud638\ucd9c \ud69f\uc218, <code>move_outside<\/code> \ud568\uc218 \ud638\ucd9c \ud69f\uc218, <code>press_button<\/code> \ud568\uc218 \ud638\ucd9c \ud69f\uc218 \uc138 \uac12 \uc911  <strong>\ucd5c\ub300\uac12<\/strong>\uc774\ub77c\uace0 \ud558\uc790.<\/p>\r\n\r\n<p>\uc11c\ube0c\ud0dc\uc2a4\ud06c 3\uc5d0\uc11c\ub294 \ubd80\ubd84 \uc810\uc218\uac00 \uc788\ub2e4. $m$\uc774 \uc774 \uc11c\ube0c\ud0dc\uc2a4\ud06c\uc758 \ubaa8\ub4e0 \ud14c\uc2a4\ud2b8\ucf00\uc774\uc2a4\uc5d0\uc11c $\\frac{q}{N}$\uc758 \ucd5c\ub300\uac12\uc774\ub77c\uace0 \ud558\uc790. \uc774 \uc11c\ube0c\ud0dc\uc2a4\ud06c\uc5d0\uc11c \uc5bb\uc744 \uc218 \uc788\ub294 \uc810\uc218\ub294 \ub2e4\uc74c \ud45c\uc5d0 \ub530\ub77c \uacc4\uc0b0\ub41c\ub2e4.<\/p>\r\n\r\n<table class=\"table table-bordered th-center td-center table-center-50\">\r\n\t<thead>\r\n\t\t<tr>\r\n\t\t\t<th>\uc870\uac74<\/th>\r\n\t\t\t<th>\uc810\uc218<\/th>\r\n\t\t<\/tr>\r\n\t<\/thead>\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td>$20 \\lt m$<\/td>\r\n\t\t\t<td>$0$ (CMS\uc5d0\uc11c &quot;<code>Output isn&rsquo;t correct<\/code>&quot;\ub85c \ucd9c\ub825)<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>$6 \\lt m \\le 20$<\/td>\r\n\t\t\t<td>$\\frac{225}{m - 2}$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>$3 \\lt m \\le 6$<\/td>\r\n\t\t\t<td>$81 - \\frac{2}{3} m^2$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>$m \\le 3$<\/td>\r\n\t\t\t<td>$75$<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n","custom_samplegrader":"<p>$T$\uac00 \uae38\uc774 $N$\uc778 \uc815\uc218 \ubc30\uc5f4\uc774\uace0 $T[i]$\uac00 \uace4\ucda9 $i$\uc758 \uc885\ub958\ub77c\uace0 \ud558\uc790.<\/p>\r\n\r\n<p>\uc0d8\ud50c \uadf8\ub808\uc774\ub354\ub294 \ub2e4\uc74c \uc591\uc2dd\uc73c\ub85c \uc785\ub825\uc744 \uc77d\ub294\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>line $1$: $N$<\/li>\r\n\t<li>line $2$: $T[0] \\, T[1] \\, \\ldots \\, T[N - 1]$<\/li>\r\n<\/ul>\r\n\r\n<p>\ub9cc\uc57d \uc0d8\ud50c \uadf8\ub808\uc774\ub354\uac00 \ud504\ub85c\ud1a0\ucf5c\uc774 \uc704\ubc18\ub41c \uac83\uc744 \ubc1c\uacac\ud558\uba74, \uc0d8\ud50c \uadf8\ub808\uc774\ub354\ub294 <code>Protocol Violation: &lt;MSG&gt;<\/code>\ub97c \ucd9c\ub825\ud558\ub294\ub370,<code>&lt;MSG&gt;<\/code>\ub294 \ub2e4\uc74c \uc911 \ud558\ub098\uc774\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li><code>invalid parameter<\/code>: <code>move_inside<\/code> \ub610\ub294 <code>move_outside<\/code>\ub97c \ud638\ucd9c\ud560 \ub54c, $i$ \uac12\uc774 $0$ \uc774\uc0c1 $N - 1$ \uc774\ud558\uac00 \uc544\ub2c8\ub2e4.<\/li>\r\n\t<li><code>too many calls<\/code>: <code>move_inside<\/code>, <code>move_outside<\/code>, <code>press_button<\/code> \uc911 <strong>\uc5b4\ub5a4 \ud55c<\/strong> \ud568\uc218\uac00 $40\\,000$ \ubc88 \ucd08\uacfc\ub418\uc5b4 \ud638\ucd9c\ub418\uc5c8\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uadf8 \uc678\uc758 \uacbd\uc6b0\uc5d0\ub294, \uc0d8\ud50c \uadf8\ub808\uc774\ub354\ub294 \ub2e4\uc74c \uc591\uc2dd\uc5d0 \ub530\ub77c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>line $1$: <code>min_cardinality<\/code>\uc758 \ub9ac\ud134\uac12<\/li>\r\n\t<li>line $2$: $q$<\/li>\r\n<\/ul>\r\n","custom_attachemtn":"<ul>\r\n\t<li><a href=\"https:\/\/upload.acmicpc.net\/5c7c93f6-7e2f-4bc9-9659-7b51b54fff5c\/\">insects.zip<\/a><\/li>\r\n<\/ul>\r\n"},{"problem_id":"25442","problem_lang":"1","title":"Rarest Insects","description":"<p>There are $N$ insects, indexed from $0$ to $N - 1$, running around Pak Blangkon&#39;s house. Each insect has a&nbsp;<strong>type<\/strong>, which is an integer between $0$ and $10^9$ inclusive. Multiple insects may have the same type.<\/p>\r\n\r\n<p>Suppose insects are grouped by type. We define the cardinality of the&nbsp;<strong>most frequent<\/strong>&nbsp;insect type as the number of insects in a group with the most number of insects. Similarly, the cardinality of the&nbsp;<strong>rarest<\/strong>insect type is the number of insects in a group with the least number of insects.<\/p>\r\n\r\n<p>For example, suppose that there are $11$ insects, whose types are $[5, 7, 9, 11, 11, 5, 0, 11, 9, 100, 9]$. In this case, the cardinality of the&nbsp;<strong>most frequent<\/strong>&nbsp;insect type is $3$. The groups with the most number of insects are type $9$ and type $11$, each consisting of $3$ insects. The cardinality of the&nbsp;<strong>rarest<\/strong>&nbsp;insect type is $1$. The groups with the least number of insects are type $7$, type $0$, and type $100$, each consisting of $1$ insect.<\/p>\r\n\r\n<p>Pak Blangkon does not know the type of any insect. He has a machine with a single button that can provide some information about the types of the insects. Initially, the machine is empty. To use the machine, three types of operations can be performed:<\/p>\r\n\r\n<ol>\r\n\t<li>Move an insect to inside the machine.<\/li>\r\n\t<li>Move an insect to outside the machine.<\/li>\r\n\t<li>Press the button on the machine.<\/li>\r\n<\/ol>\r\n\r\n<p>Each type of operation can be performed at most $40\\,000$ times.<\/p>\r\n\r\n<p>Whenever the button is pressed, the machine reports the cardinality of the&nbsp;<strong>most frequent<\/strong>&nbsp;insect type, considering only insects inside the machine.<\/p>\r\n\r\n<p>Your task is to determine the cardinality of the&nbsp;<strong>rarest<\/strong>&nbsp;insect type among all $N$ insects in Pak Blangkon&#39;s house by using the machine. Additionally, in some subtasks, your score depends on the maximum number of operations of a given type that are performed (see Subtasks section for details).<\/p>\r\n","input":"","output":"","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>$2 \\le N \\le 2000$<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$N \\le 200$<\/p>\r\n","subtask2":"<p>$N \\le 1000$<\/p>\r\n","subtask3":"<p>No additional constraints.<\/p>\r\n","custom_implementation":"<p>You should implement the following procedure:<\/p>\r\n\r\n<pre>\r\n<code>int min_cardinality(int N)\r\n<\/code><\/pre>\r\n\r\n<ul>\r\n\t<li>$N$: the number of insects.<\/li>\r\n\t<li>This procedure should return the cardinality of the <strong>rarest<\/strong> insect type among all $N$ insects in Pak Blangkon&#39;s house.<\/li>\r\n\t<li>This procedure is called exactly once.<\/li>\r\n<\/ul>\r\n\r\n<p>The above procedure can make calls to the following procedures:<\/p>\r\n\r\n<pre>\r\n<code>void move_inside(int i)\r\n<\/code><\/pre>\r\n\r\n<ul>\r\n\t<li>$i$: the index of the insect to be moved inside the machine. The value of $i$ must be between $0$ and $N - 1$ inclusive.<\/li>\r\n\t<li>If this insect is already inside the machine, the call has no effect on the set of insects in the machine. However, it is still counted as a separate call.<\/li>\r\n\t<li>This procedure can be called at most $40\\,000$ times.<\/li>\r\n<\/ul>\r\n\r\n<pre>\r\n<code>void move_outside(int i)\r\n<\/code><\/pre>\r\n\r\n<ul>\r\n\t<li>$i$: the index of the insect to be moved outside the machine. The value of $i$ must be between $0$ and $N - 1$ inclusive.<\/li>\r\n\t<li>If this insect is already outside the machine, the call has no effect on the set of insects in the machine. However, it is still counted as a separate call.<\/li>\r\n\t<li>This procedure can be called at most $40\\,000$ times.<\/li>\r\n<\/ul>\r\n\r\n<pre>\r\n<code>int press_button()\r\n<\/code><\/pre>\r\n\r\n<ul>\r\n\t<li>This procedure returns the cardinality of the <strong>most frequent<\/strong> insect type, considering only insects inside the machine.<\/li>\r\n\t<li>This procedure can be called at most $40\\,000$ times.<\/li>\r\n\t<li>The grader is <strong>not adaptive<\/strong>. That is, the types of all $N$ insects are fixed before <code>min_cardinality<\/code> is called.\\,<\/li>\r\n<\/ul>\r\n","custom_example":"<p>Consider a scenario in which there are $6$ insects of types $[5, 8, 9, 5, 9, 9]$ respectively. The procedure <code>min_cardinality<\/code> is called in the following way:<\/p>\r\n\r\n<pre>\r\n<code>min_cardinality(6)\r\n<\/code><\/pre>\r\n\r\n<p>The procedure may call <code>move_inside<\/code>, <code>move_outside<\/code>, and <code>press_button<\/code> as follows.<\/p>\r\n\r\n<table class=\"table table-bordered td-center th-center\">\r\n\t<thead>\r\n\t\t<tr>\r\n\t\t\t<th>Call<\/th>\r\n\t\t\t<th>Return value<\/th>\r\n\t\t\t<th>Insects in the machine<\/th>\r\n\t\t\t<th>Types of insects in the machine<\/th>\r\n\t\t<\/tr>\r\n\t<\/thead>\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td> <\/td>\r\n\t\t\t<td>$\\{\\}$<\/td>\r\n\t\t\t<td>$[]$<\/td>\r\n\t\t\t<td> <\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>move_inside(0)<\/code><\/td>\r\n\t\t\t<td> <\/td>\r\n\t\t\t<td>$\\{0\\}$<\/td>\r\n\t\t\t<td>$[5]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>press_button()<\/code><\/td>\r\n\t\t\t<td>$1$<\/td>\r\n\t\t\t<td>$\\{0\\}$<\/td>\r\n\t\t\t<td>$[5]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>move_inside(1)<\/code><\/td>\r\n\t\t\t<td> <\/td>\r\n\t\t\t<td>$\\{0, 1\\}$<\/td>\r\n\t\t\t<td>$[5, 8]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>press_button()<\/code><\/td>\r\n\t\t\t<td>$1$<\/td>\r\n\t\t\t<td>$\\{0, 1\\}$<\/td>\r\n\t\t\t<td>$[5, 8]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>move_inside(3)<\/code><\/td>\r\n\t\t\t<td> <\/td>\r\n\t\t\t<td>$\\{0, 1, 3\\}$<\/td>\r\n\t\t\t<td>$[5, 8, 5]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>press_button()<\/code><\/td>\r\n\t\t\t<td>$2$<\/td>\r\n\t\t\t<td>$\\{0, 1, 3\\}$<\/td>\r\n\t\t\t<td>$[5, 8, 5]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>move_inside(2)<\/code><\/td>\r\n\t\t\t<td> <\/td>\r\n\t\t\t<td>$\\{0, 1, 2, 3\\}$<\/td>\r\n\t\t\t<td>$[5, 8, 9, 5]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>move_inside(4)<\/code><\/td>\r\n\t\t\t<td> <\/td>\r\n\t\t\t<td>$\\{0, 1, 2, 3, 4\\}$<\/td>\r\n\t\t\t<td>$[5, 8, 9, 5, 9]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>move_inside(5)<\/code><\/td>\r\n\t\t\t<td> <\/td>\r\n\t\t\t<td>$\\{0, 1, 2, 3, 4, 5\\}$<\/td>\r\n\t\t\t<td>$[5, 8, 9, 5, 9, 9]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>press_button()<\/code><\/td>\r\n\t\t\t<td>$3$<\/td>\r\n\t\t\t<td>$\\{0, 1, 2, 3, 4, 5\\}$<\/td>\r\n\t\t\t<td>$[5, 8, 9, 5, 9, 9]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>move_inside(5)<\/code><\/td>\r\n\t\t\t<td> <\/td>\r\n\t\t\t<td>$\\{0, 1, 2, 3, 4, 5\\}$<\/td>\r\n\t\t\t<td>$[5, 8, 9, 5, 9, 9]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>press_button()<\/code><\/td>\r\n\t\t\t<td>$3$<\/td>\r\n\t\t\t<td>$\\{0, 1, 2, 3, 4, 5\\}$<\/td>\r\n\t\t\t<td>$[5, 8, 9, 5, 9, 9]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>move_outside(5)<\/code><\/td>\r\n\t\t\t<td> <\/td>\r\n\t\t\t<td>$\\{0, 1, 2, 3, 4\\}$<\/td>\r\n\t\t\t<td>$[5, 8, 9, 5, 9]$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td><code>press_button()<\/code><\/td>\r\n\t\t\t<td>$2$<\/td>\r\n\t\t\t<td>$\\{0, 1, 2, 3, 4\\}$<\/td>\r\n\t\t\t<td>$[5, 8, 9, 5, 9]$<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>At this point, there is sufficient information to conclude that the cardinality of the rarest insect type is $1$. Therefore, the procedure <code>min_cardinality<\/code> should return $1$.<\/p>\r\n\r\n<p>In this example, <code>move_inside<\/code> is called $7$ times, <code>move_outside<\/code> is called $1$ time, and <code>press_button<\/code> is called $6$ times.<\/p>\r\n","custom_subtask_scoring_a":"<p>If in any of the test cases, the calls to the procedures <code>move_inside<\/code>, <code>move_outside<\/code>, or <code>press_button<\/code> do not conform to the constraints described in Implementation Details, or the return value of <code>min_cardinality<\/code> is incorrect, the score of your solution for that subtask will be $0$.<\/p>\r\n\r\n<p>Let $q$ be the <strong>maximum<\/strong> of the following three values: the number of calls to <code>move_inside<\/code>, the number of calls to <code>move_outside<\/code>, and the number of calls to <code>press_button<\/code>.<\/p>\r\n\r\n<p>In subtask 3, you can obtain a partial score. Let $m$ be the maximum value of $\\frac{q}{N}$ across all test cases in this subtask. Your score for this subtask is calculated according to the following table:<\/p>\r\n\r\n<table class=\"table table-bordered th-center td-center table-center-50\">\r\n\t<thead>\r\n\t\t<tr>\r\n\t\t\t<th>Condition<\/th>\r\n\t\t\t<th>Points<\/th>\r\n\t\t<\/tr>\r\n\t<\/thead>\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td>$20 \\lt m$<\/td>\r\n\t\t\t<td>$0$ (reported as &quot;<code>Output isn&rsquo;t correct<\/code>&quot; in CMS)<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>$6 \\lt m \\le 20$<\/td>\r\n\t\t\t<td>$\\frac{225}{m - 2}$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>$3 \\lt m \\le 6$<\/td>\r\n\t\t\t<td>$81 - \\frac{2}{3} m^2$<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>$m \\le 3$<\/td>\r\n\t\t\t<td>$75$<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n","custom_samplegrader":"<p>Let $T$ be an array of $N$ integers where $T[i]$ is the type of insect $i$.<\/p>\r\n\r\n<p>The sample grader reads the input in the following format:<\/p>\r\n\r\n<ul>\r\n\t<li>line $1$: $N$<\/li>\r\n\t<li>line $2$: $T[0] \\, T[1] \\, \\ldots \\, T[N - 1]$<\/li>\r\n<\/ul>\r\n\r\n<p>If the sample grader detects a protocol violation, the output of the sample grader is <code>Protocol Violation: &lt;MSG&gt;<\/code>, where <code>&lt;MSG&gt;<\/code> is one of the following:<\/p>\r\n\r\n<ul>\r\n\t<li><code>invalid parameter<\/code>: in a call to <code>move_inside<\/code> or <code>move_outside<\/code>, the value of $i$ is not between $0$ and $N - 1$ inclusive.<\/li>\r\n\t<li><code>too many calls<\/code>: the number of calls to <strong>any<\/strong> of <code>move_inside<\/code>, <code>move_outside<\/code>, or <code>press_button<\/code> exceeds $40\\,000$.<\/li>\r\n<\/ul>\r\n\r\n<p>Otherwise, the output of the sample grader is in the following format:<\/p>\r\n\r\n<ul>\r\n\t<li>line $1$: the return value of <code>min_cardinality<\/code><\/li>\r\n\t<li>line $2$: $q$<\/li>\r\n<\/ul>\r\n","custom_attachemtn":"<ul>\r\n\t<li><a href=\"https:\/\/upload.acmicpc.net\/5c7c93f6-7e2f-4bc9-9659-7b51b54fff5c\/\">insects.zip<\/a><\/li>\r\n<\/ul>\r\n"}]

샘플 그레이더

$T$가 길이 $N$인 정수 배열이고 $T[i]$가 곤충 $i$의 종류라고 하자.

샘플 그레이더는 다음 양식으로 입력을 읽는다.

  • line $1$: $N$
  • line $2$: $T[0] \, T[1] \, \ldots \, T[N - 1]$

만약 샘플 그레이더가 프로토콜이 위반된 것을 발견하면, 샘플 그레이더는 Protocol Violation: <MSG>를 출력하는데,<MSG>는 다음 중 하나이다.

  • invalid parameter: move_inside 또는 move_outside를 호출할 때, $i$ 값이 $0$ 이상 $N - 1$ 이하가 아니다.
  • too many calls: move_inside, move_outside, press_button어떤 한 함수가 $40\,000$ 번 초과되어 호출되었다.

그 외의 경우에는, 샘플 그레이더는 다음 양식에 따라 출력한다.

  • line $1$: min_cardinality의 리턴값
  • line $2$: $q$

첨부

출처

Olympiad > International Olympiad in Informatics > IOI 2022 > Day 2 5번

  • 문제를 만든 사람: Hazem Issa

제출할 수 있는 언어

C++17, C++20, C++17 (Clang), C++20 (Clang)

채점 및 기타 정보

  • 예제는 채점하지 않는다.