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문제

알버트가 다니는 학교에서 곧 해커톤이 열린다. 이 해커톤에는 N명의 학생이 참가 의사를 밝혔다. 편의상 학생에 번호를 매겼고, 번호는 1부터 N까지이다. 

해커톤에 참가하는 N명을 몇 개의 팀으로 나눠야 하는데, 대회 주최 측에서는 팀의 개수를 최소로 하고싶어 한다. 단, i번 학생은 자신이 속한 팀의 팀원 수가 자기 자신을 포함해서 Xi명 이하일 때만 참가한다고 한다. 주최 측은 참가 의사를 밝힌 N명이 모두 참여할 수 있도록 팀을 배정할 생각이며, 이 때 팀의 수를 최소로 하려고 한다.

다음 조건을 모두 만족하게 팀을 만들어야 한다.

  • 한 학생은 하나의 팀에 소속되어야 한다.
  • 각 팀은 최소 한 명의 학생을 포함한다.
  • 모든 i에 대해서, i번 학생이 속한 팀의 팀원 수는 Xi명 이하이어야 한다.

위의 조건을 만족하면서 N명을 팀으로 나눴을 때, 팀의 수의 최솟값을 구하는 프로그램을 작성하시오.

입력

첫째 줄에는 학생의 수 N(1 ≤ N ≤ 100,000)이 주어진다.

둘째 줄에는 N개의 정수가 주어지고, 순서대로 X1, X2, ..., XN을 의미한다. 모든 i에 대해서, 1 ≤ Xi ≤ N을 만족한다.

출력

첫째 줄에 팀의 수의 최솟값을 출력한다.

예제 입력 1

2
2 2

예제 출력 1

1

예제 입력 2

5
1 2 5 2 1

예제 출력 2

4

예제 입력 3

5
1 2 1 2 1

예제 출력 3

4

예제 입력 4

9
2 2 2 3 3 3 2 2 2

예제 출력 4

4

다음과 같이 4팀을 만들 수 있다.

{1, 9}, {2, 8}, {3, 7}, {4, 5, 6}

예제 입력 5

9
2 2 2 2 2 3 3 3 3

예제 출력 5

4

다음과 같이 4팀을 만들 수 있다.

{1, 2}, {3, 4}, {5, 6}, {7, 8, 9}

힌트

예를 들어, 5명의 학생이 있고, X1 = 1, X2 = 2, X3 = 5, X4 = 2, X5 = 1인 경우에 팀의 수의 최솟값은 4이다.

{1}, {2}, {3}, {4}, {5}로 5개의 팀을 만드는 방법이 있지만, 이것은 팀의 수가 최소가 아니다. {1}, {3}, {5}, {2, 4}와 같이 팀을 만들면, 문제의 조건을 모두 만족하고, 팀의 수도 최소이다.

[{"problem_id":"16200","problem_lang":"0","title":"\ud574\ucee4\ud1a4","description":"<p>\uc54c\ubc84\ud2b8\uac00 \ub2e4\ub2c8\ub294 \ud559\uad50\uc5d0\uc11c \uace7 \ud574\ucee4\ud1a4\uc774 \uc5f4\ub9b0\ub2e4. \uc774 \ud574\ucee4\ud1a4\uc5d0\ub294 N\uba85\uc758 \ud559\uc0dd\uc774 \ucc38\uac00 \uc758\uc0ac\ub97c \ubc1d\ud614\ub2e4.&nbsp;\ud3b8\uc758\uc0c1 \ud559\uc0dd\uc5d0 \ubc88\ud638\ub97c \ub9e4\uacbc\uace0, \ubc88\ud638\ub294 1\ubd80\ud130 N\uae4c\uc9c0\uc774\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\ud574\ucee4\ud1a4\uc5d0 \ucc38\uac00\ud558\ub294 N\uba85\uc744 \uba87 \uac1c\uc758 \ud300\uc73c\ub85c \ub098\ub220\uc57c \ud558\ub294\ub370, \ub300\ud68c \uc8fc\ucd5c \uce21\uc5d0\uc11c\ub294 \ud300\uc758 \uac1c\uc218\ub97c \ucd5c\uc18c\ub85c \ud558\uace0\uc2f6\uc5b4 \ud55c\ub2e4. \ub2e8, i\ubc88 \ud559\uc0dd\uc740 \uc790\uc2e0\uc774 \uc18d\ud55c \ud300\uc758 \ud300\uc6d0 \uc218\uac00 \uc790\uae30 \uc790\uc2e0\uc744 \ud3ec\ud568\ud574\uc11c X<sub>i<\/sub>\uba85 \uc774\ud558\uc77c \ub54c\ub9cc \ucc38\uac00\ud55c\ub2e4\uace0 \ud55c\ub2e4. \uc8fc\ucd5c \uce21\uc740 \ucc38\uac00 \uc758\uc0ac\ub97c \ubc1d\ud78c N\uba85\uc774 \ubaa8\ub450 \ucc38\uc5ec\ud560 \uc218 \uc788\ub3c4\ub85d \ud300\uc744 \ubc30\uc815\ud560 \uc0dd\uac01\uc774\uba70, \uc774 \ub54c \ud300\uc758 \uc218\ub97c \ucd5c\uc18c\ub85c \ud558\ub824\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c \uc870\uac74\uc744 \ubaa8\ub450 \ub9cc\uc871\ud558\uac8c \ud300\uc744 \ub9cc\ub4e4\uc5b4\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\ud55c \ud559\uc0dd\uc740 \ud558\ub098\uc758 \ud300\uc5d0 \uc18c\uc18d\ub418\uc5b4\uc57c \ud55c\ub2e4.<\/li>\r\n\t<li>\uac01 \ud300\uc740 \ucd5c\uc18c \ud55c \uba85\uc758 \ud559\uc0dd\uc744 \ud3ec\ud568\ud55c\ub2e4.<\/li>\r\n\t<li>\ubaa8\ub4e0 i\uc5d0 \ub300\ud574\uc11c, i\ubc88 \ud559\uc0dd\uc774 \uc18d\ud55c \ud300\uc758 \ud300\uc6d0 \uc218\ub294 X<sub>i<\/sub>\uba85 \uc774\ud558\uc774\uc5b4\uc57c \ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc704\uc758 \uc870\uac74\uc744 \ub9cc\uc871\ud558\uba74\uc11c N\uba85\uc744 \ud300\uc73c\ub85c \ub098\ub234\uc744 \ub54c, \ud300\uc758 \uc218\uc758 \ucd5c\uc19f\uac12\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0\ub294 \ud559\uc0dd\uc758 \uc218 N(1 &le; N &le; 100,000)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\uc5d0\ub294 N\uac1c\uc758 \uc815\uc218\uac00 \uc8fc\uc5b4\uc9c0\uace0, \uc21c\uc11c\ub300\ub85c X<sub>1<\/sub>, X<sub>2<\/sub>, ..., X<sub>N<\/sub>\uc744 \uc758\ubbf8\ud55c\ub2e4. \ubaa8\ub4e0 i\uc5d0 \ub300\ud574\uc11c, 1 &le; X<sub>i<\/sub> &le; N\uc744 \ub9cc\uc871\ud55c\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud300\uc758 \uc218\uc758 \ucd5c\uc19f\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\uc608\ub97c \ub4e4\uc5b4, 5\uba85\uc758 \ud559\uc0dd\uc774 \uc788\uace0, X<sub>1<\/sub> = 1, X<sub>2<\/sub> = 2, X<sub>3<\/sub> = 5, X<sub>4<\/sub> = 2, X<sub>5<\/sub> = 1\uc778 \uacbd\uc6b0\uc5d0 \ud300\uc758 \uc218\uc758 \ucd5c\uc19f\uac12\uc740 4\uc774\ub2e4.<\/p>\r\n\r\n<p>{1}, {2}, {3}, {4}, {5}\ub85c 5\uac1c\uc758 \ud300\uc744 \ub9cc\ub4dc\ub294 \ubc29\ubc95\uc774 \uc788\uc9c0\ub9cc, \uc774\uac83\uc740 \ud300\uc758 \uc218\uac00&nbsp;\ucd5c\uc18c\uac00 \uc544\ub2c8\ub2e4. {1}, {3}, {5}, {2, 4}\uc640 \uac19\uc774 \ud300\uc744 \ub9cc\ub4e4\uba74, \ubb38\uc81c\uc758 \uc870\uac74\uc744 \ubaa8\ub450 \ub9cc\uc871\ud558\uace0, \ud300\uc758 \uc218\ub3c4 \ucd5c\uc18c\uc774\ub2e4.<\/p>\r\n","original":"1","problem_lang_code":"\ud55c\uad6d\uc5b4","sample_explain_4":"<p>\ub2e4\uc74c\uacfc \uac19\uc774 4\ud300\uc744 \ub9cc\ub4e4 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>{1, 9}, {2, 8}, {3, 7}, {4, 5, 6}<\/p>\r\n","sample_explain_5":"<p>\ub2e4\uc74c\uacfc \uac19\uc774 4\ud300\uc744 \ub9cc\ub4e4 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>{1, 2}, {3, 4}, {5, 6}, {7, 8, 9}<\/p>\r\n"},{"problem_id":"16200","problem_lang":"1","title":"Team Formation","description":"<p>Albert&#39;s school is hosting a hackathon event for students. There are N students who wish to participate in the event. Let&#39;s label the students as 1, 2, ..., N.<\/p>\r\n\r\n<p>Student i wants to participate in the event&nbsp;if and only if the team he\/she belongs to has at most X<sub>i<\/sub> members in it (including student i). Because the space is limited at the event venue, the school needs to minimize the number of teams. More precisely, Albert wants to compute the minimum number of teams while meeting the following conditions:<\/p>\r\n\r\n<ul>\r\n\t<li>Every student is assigned to exactly one team<\/li>\r\n\t<li>Each team contains at least one student<\/li>\r\n\t<li>If student i belongs to a team, then the number of students in the team (including student i) is no greater than X<sub>i<\/sub>.<\/li>\r\n<\/ul>\r\n\r\n<p>Albert needs to help his school host the event successfully, and you need to help Albert determine the minimum number of teams that can be formed given students&#39; constraints.&nbsp;<\/p>\r\n","input":"<p>The first line will contain the number of students, N (1 &le; N &le; 100,000).<\/p>\r\n\r\n<p>The second line will contain N integers representing X<sub>i<\/sub> values for each student. Assume that 1 &le;&nbsp;X<sub>i<\/sub> &le;&nbsp;N for all i&#39;s.<\/p>\r\n","output":"<p>You should output a single number, representing the minimum number of teams that can be formed.<\/p>\r\n","hint":"<p>For instance, suppose there are five students (N = 5) with X<sub>1<\/sub> = 1, X<sub>2<\/sub> = 2, X<sub>3<\/sub> = 5, X<sub>4<\/sub> = 2, and X<sub>5<\/sub> = 1. In particular, student 3 wishes to be in a team with at most 5 members, whereas students 2 and 4 at most 2 students.&nbsp;<\/p>\r\n\r\n<p>One (trivial) way to form teams is to let each student form a 1-person team -- this yields five teams. Or, we can let students 2 and 4 form one team, and the other three students form 1-person teams -- this results in four teams. In this example, there is no way to form 3 or fewer teams while meeting the said conditions.<\/p>\r\n","original":"0","problem_lang_code":"\uc601\uc5b4","sample_explain_4":"<p>Here is one solution to assign students to four teams:<\/p>\r\n\r\n<p>{1, 9}, {2, 8}, {3, 7}, {4, 5, 6}.<\/p>\r\n","sample_explain_5":"<p>Here is one solution to assign students to four teams:<\/p>\r\n\r\n<p>{1, 2}, {3, 4}, {5, 6}, {7, 8, 9}.<\/p>\r\n"}]

출처

  • 문제를 만든 사람: haden
  • 잘못된 데이터를 찾은 사람: tncks0121