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34094번 - 골드리치의 비밀 금고 스페셜 저지다국어

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2 초 (추가 시간 없음) 1024 MB (추가 메모리 없음)40816413940.058%

문제

골드리치는 메이플 용사들을 위해 새로운 비밀 금고 이벤트를 열었다. 메이플 용사는 각자 금고에 비밀번호를 입력해 이벤트에 응모하게 된다. 기존의 황금 금고, 다이아 금고 이벤트에서는 응모된 비밀번호 중 중복되지 않는 작은 수를 입력한 용사들에게 상품을 지급했다.

골드리치는 이번 루비 금고 이벤트에서 큰돈을 들여 모든 용사에게 같은 개수의 상품을 지급할 계획이다. 대신 각 용사가 받을 상품 개수는 용사들이 입력하는 비밀번호에 따라 달라진다. 상품 개수를 결정하는 방식은 아래와 같다.

  • 각 용사 $i$는 정수 $A_i$를 비밀번호로 입력한다. $(0 \le A_i \le 10^9$; 1ドル \le i \le N)$
  • $[A_l, A_{l + 1}, \cdots, A_{r-1}, A_r]$에서 존재하지 않는 가장 작은 음이 아닌 정수를 $C_{lr}$라고 한다. $(1 \le l \le r \le N)$
  • 가능한 $C_{lr}$ 중 존재하지 않는 가장 작은 음이 아닌 정수가 각 용사가 받을 상품 개수가 된다.

$\{C_{11},C_{22},C_{33},C_{12},C_{23},C_{13}\} = \{0,0,1,0,1,3\} \rightarrow 2$

메이플 용사들은 단합하여 최대한 많은 상품을 받으려 했지만, 용사의 수가 너무나 많은 까닭에 의견을 모으지 못한 채로 비밀번호를 모두 입력해 버리고 말았다.

메이플 용사로서 루비 금고 이벤트에 참가한 팬텀 역시 더 많은 상품을 원하고 있었다. 비밀번호가 모두 입력된 것을 본 팬텀은, 메이플 월드 최고의 괴도답게 비밀번호를 조작해서 받게 될 상품 수를 최대한 크게 만드는 작전을 세웠다.

다른 용사가 입력한 비밀번호를 바꾸는 것은 팬텀에게는 쉬운 일이지만, 금방 발각될 위험이 있기 때문에 입력된 비밀번호 $A_1, A_2, \cdots, A_N$의 순서만 바꾸려고 한다.

상품 개수가 최대가 되도록 팬텀이 재배열한 순서를 구해 보자.

입력

첫째 줄에 이벤트에 응모한 메이플 용사의 인원 수 $N$이 주어진다. (1ドル \le N \le 1,円 000,円 000$)

둘째 줄에 $N$개의 정수 $A_1, A_2, \cdots, A_N$이 공백으로 구분되어 주어진다. (0ドル \le A_i \le 10^9$)

출력

첫째 줄에 만들 수 있는 최대 상품 개수를 출력한다.

둘째 줄에 그때의 재배열된 $A_1, A_2, \cdots, A_N$을 공백으로 구분하여 출력한다. 가능한 답이 여러 개라면 그중 아무 것이나 출력한다.

제한

예제 입력 1

3
1 2 0

예제 출력 1

4
1 0 2

예제 입력 2

3
1 3 0

예제 출력 2

3
1 3 0

힌트

[{"problem_id":"34094","problem_lang":"0","title":"\uace8\ub4dc\ub9ac\uce58\uc758 \ube44\ubc00 \uae08\uace0","description":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/a485df9c-019d-4a69-816e-8bf3a4b3fe66\/-\/preview\/\" \/><\/p>\r\n\r\n<p>\uace8\ub4dc\ub9ac\uce58\ub294 \uba54\uc774\ud50c \uc6a9\uc0ac\ub4e4\uc744 \uc704\ud574 \uc0c8\ub85c\uc6b4 \ube44\ubc00 \uae08\uace0 \uc774\ubca4\ud2b8\ub97c \uc5f4\uc5c8\ub2e4. \uba54\uc774\ud50c \uc6a9\uc0ac\ub294 \uac01\uc790 \uae08\uace0\uc5d0 \ube44\ubc00\ubc88\ud638\ub97c \uc785\ub825\ud574 \uc774\ubca4\ud2b8\uc5d0 \uc751\ubaa8\ud558\uac8c \ub41c\ub2e4. \uae30\uc874\uc758 \ud669\uae08 \uae08\uace0, \ub2e4\uc774\uc544 \uae08\uace0 \uc774\ubca4\ud2b8\uc5d0\uc11c\ub294 \uc751\ubaa8\ub41c \ube44\ubc00\ubc88\ud638 \uc911 \uc911\ubcf5\ub418\uc9c0 \uc54a\ub294 \uc791\uc740 \uc218\ub97c \uc785\ub825\ud55c \uc6a9\uc0ac\ub4e4\uc5d0\uac8c \uc0c1\ud488\uc744 \uc9c0\uae09\ud588\ub2e4.<\/p>\r\n\r\n<p>\uace8\ub4dc\ub9ac\uce58\ub294 \uc774\ubc88 \ub8e8\ube44 \uae08\uace0 \uc774\ubca4\ud2b8\uc5d0\uc11c \ud070\ub3c8\uc744 \ub4e4\uc5ec \ubaa8\ub4e0 \uc6a9\uc0ac\uc5d0\uac8c \uac19\uc740 \uac1c\uc218\uc758 \uc0c1\ud488\uc744 \uc9c0\uae09\ud560 \uacc4\ud68d\uc774\ub2e4. \ub300\uc2e0 \uac01 \uc6a9\uc0ac\uac00 \ubc1b\uc744 \uc0c1\ud488 \uac1c\uc218\ub294 \uc6a9\uc0ac\ub4e4\uc774 \uc785\ub825\ud558\ub294 \ube44\ubc00\ubc88\ud638\uc5d0 \ub530\ub77c \ub2ec\ub77c\uc9c4\ub2e4. \uc0c1\ud488 \uac1c\uc218\ub97c \uacb0\uc815\ud558\ub294 \ubc29\uc2dd\uc740 \uc544\ub798\uc640 \uac19\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uac01 \uc6a9\uc0ac $i$\ub294 \uc815\uc218 $A_i$\ub97c \ube44\ubc00\ubc88\ud638\ub85c \uc785\ub825\ud55c\ub2e4. $(0 \\le A_i \\le 10^9$; $1 \\le i \\le N)$<\/li>\r\n\t<li>$[A_l, A_{l + 1}, \\cdots, A_{r-1}, A_r]$\uc5d0\uc11c \uc874\uc7ac\ud558\uc9c0 \uc54a\ub294 \uac00\uc7a5 \uc791\uc740 \uc74c\uc774 \uc544\ub2cc \uc815\uc218\ub97c $C_{lr}$\ub77c\uace0 \ud55c\ub2e4. $(1 \\le l \\le r \\le N)$<\/li>\r\n\t<li>\uac00\ub2a5\ud55c $C_{lr}$ \uc911 \uc874\uc7ac\ud558\uc9c0 \uc54a\ub294 \uac00\uc7a5 \uc791\uc740 \uc74c\uc774 \uc544\ub2cc \uc815\uc218\uac00 \uac01 \uc6a9\uc0ac\uac00 \ubc1b\uc744 \uc0c1\ud488 \uac1c\uc218\uac00 \ub41c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/57ce2b74-7116-4b0d-8c06-485c15c64381\/-\/preview\/\" style=\"height: 224px; width: 1000px;\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">$\\{C_{11},C_{22},C_{33},C_{12},C_{23},C_{13}\\} = \\{0,0,1,0,1,3\\} \\rightarrow 2$<\/p>\r\n\r\n<p>\uba54\uc774\ud50c \uc6a9\uc0ac\ub4e4\uc740 \ub2e8\ud569\ud558\uc5ec \ucd5c\ub300\ud55c \ub9ce\uc740 \uc0c1\ud488\uc744 \ubc1b\uc73c\ub824 \ud588\uc9c0\ub9cc, \uc6a9\uc0ac\uc758 \uc218\uac00 \ub108\ubb34\ub098 \ub9ce\uc740 \uae4c\ub2ed\uc5d0 \uc758\uacac\uc744 \ubaa8\uc73c\uc9c0 \ubabb\ud55c \ucc44\ub85c \ube44\ubc00\ubc88\ud638\ub97c \ubaa8\ub450 \uc785\ub825\ud574 \ubc84\ub9ac\uace0 \ub9d0\uc558\ub2e4.<\/p>\r\n\r\n<p>\uba54\uc774\ud50c \uc6a9\uc0ac\ub85c\uc11c \ub8e8\ube44 \uae08\uace0 \uc774\ubca4\ud2b8\uc5d0 \ucc38\uac00\ud55c \ud32c\ud140 \uc5ed\uc2dc \ub354 \ub9ce\uc740 \uc0c1\ud488\uc744 \uc6d0\ud558\uace0 \uc788\uc5c8\ub2e4. \ube44\ubc00\ubc88\ud638\uac00 \ubaa8\ub450 \uc785\ub825\ub41c \uac83\uc744 \ubcf8 \ud32c\ud140\uc740, \uba54\uc774\ud50c \uc6d4\ub4dc \ucd5c\uace0\uc758 \uad34\ub3c4\ub2f5\uac8c \ube44\ubc00\ubc88\ud638\ub97c \uc870\uc791\ud574\uc11c \ubc1b\uac8c \ub420 \uc0c1\ud488 \uc218\ub97c \ucd5c\ub300\ud55c \ud06c\uac8c \ub9cc\ub4dc\ub294 \uc791\uc804\uc744 \uc138\uc6e0\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\ub978 \uc6a9\uc0ac\uac00 \uc785\ub825\ud55c \ube44\ubc00\ubc88\ud638\ub97c \ubc14\uafb8\ub294 \uac83\uc740 \ud32c\ud140\uc5d0\uac8c\ub294 \uc26c\uc6b4 \uc77c\uc774\uc9c0\ub9cc, \uae08\ubc29 \ubc1c\uac01\ub420 \uc704\ud5d8\uc774 \uc788\uae30 \ub54c\ubb38\uc5d0 \uc785\ub825\ub41c \ube44\ubc00\ubc88\ud638 $A_1, A_2, \\cdots, A_N$\uc758 \uc21c\uc11c\ub9cc \ubc14\uafb8\ub824\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc0c1\ud488 \uac1c\uc218\uac00 \ucd5c\ub300\uac00 \ub418\ub3c4\ub85d \ud32c\ud140\uc774 \uc7ac\ubc30\uc5f4\ud55c \uc21c\uc11c\ub97c \uad6c\ud574 \ubcf4\uc790.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc774\ubca4\ud2b8\uc5d0 \uc751\ubaa8\ud55c \uba54\uc774\ud50c \uc6a9\uc0ac\uc758 \uc778\uc6d0 \uc218 $N$\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. ($1 \\le N \\le 1\\, 000\\, 000$)<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\uc5d0 $N$\uac1c\uc758 \uc815\uc218 $A_1, A_2, \\cdots, A_N$\uc774 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. ($0 \\le A_i \\le 10^9$)<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \ub9cc\ub4e4 \uc218 \uc788\ub294 \ucd5c\ub300 \uc0c1\ud488 \uac1c\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\uc5d0 \uadf8\ub54c\uc758 \uc7ac\ubc30\uc5f4\ub41c $A_1, A_2, \\cdots, A_N$\uc744 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ud558\uc5ec \ucd9c\ub825\ud55c\ub2e4. \uac00\ub2a5\ud55c \ub2f5\uc774 \uc5ec\ub7ec \uac1c\ub77c\uba74 \uadf8\uc911 \uc544\ubb34 \uac83\uc774\ub098 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"34094","problem_lang":"1","title":"Gold Richie's Safe","description":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/a485df9c-019d-4a69-816e-8bf3a4b3fe66\/-\/preview\/\" \/><\/p>\r\n\r\n<p>Gold Richie hosted a new secret safe event for Maple warriors. Maple warriors can enter the event by each typing in a password into the safe. The gold safe, and diamond safe events which were held previously awarded prizes to warriors who entered the smallest unique number as the password.<\/p>\r\n\r\n<p>However this time, for the ruby safe event, Gold Richie plans to use a large amount of money to award all Maple Warriors an equal number of prizes. The number of prizes is determined by the passwords that the Maple Warriors have entered. The number of prizes is determined as follows.<\/p>\r\n\r\n<ul>\r\n\t<li>The $i$-th Maple warrior enters an integer $A_i$ as the password. $(0 \\le A_i \\le 10^9$; $1 \\le i \\le N)$<\/li>\r\n\t<li>Let $C_{lr}$ be the smallest non-negative integer which is not present in $[A_l, A_{l + 1}, \\cdots, A_{r-1}, A_r]$. $(1 \\le l \\le r \\le N)$<\/li>\r\n\t<li>The number of prizes is the smallest non-negative integer which is not present in the list of all possible $C_{lr}$ values.<\/li>\r\n<\/ul>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/57ce2b74-7116-4b0d-8c06-485c15c64381\/-\/preview\/\" style=\"height: 224px; width: 1000px;\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">$\\{C_{11},C_{22},C_{33},C_{12},C_{23},C_{13}\\} = \\{0,0,1,0,1,3\\} \\rightarrow 2$<\/p>\r\n\r\n<p>The Maple Warriors tried to come together to receive as many prizes as possible, but there were too many of them, and had to enter all the passwords without coming to a unified conclusion.<\/p>\r\n\r\n<p>As a Maple Warrior himself, Phantom has entered the ruby safe event, and wishes to receive as many prizes as possible. Seeing that all the passwords have been entered, Phantom, who is Maple World&#39;s best thief, has come up with a plan to modify the passwords in a way that maximizes the number of prizes to be received.<\/p>\r\n\r\n<p>It is a piece of cake for Phantom to directly change the password another Maple Warrior has entered, but this has the risk of easily being caught. Thus, he plans to only change the order of $A_1, A_2, \\cdots, A_N$, the passwords which have been entered.<\/p>\r\n\r\n<p>Find out how Phantom has rearranged the passwords such that the number of prizes is maximized.<\/p>\r\n","input":"<p>The first line of input contains $N$, denoting the number of Maple warriors who entered the event. ($1 \\le N \\le 1\\, 000\\, 000$)<\/p>\r\n\r\n<p>The second line of input contains $N$ space-separated integers $A_1, A_2, \\cdots, A_N$. ($0 \\le A_i \\le 10^9$)<\/p>\r\n","output":"<p>Print the maximum number of prizes which can be received in the first line.<\/p>\r\n\r\n<p>Print the resulting rearranged $A_1, A_2, \\cdots, A_N$, separated by spaces. If there are multiple possible answers, print any one of them.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English"}]

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University > 전국 대학생 프로그래밍 대회 동아리 연합 > UCPC 2025 I번

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