문제
NLCS Jeju에는 화재 경보가 울리면 모든 커플이 헤어진다는 징크스가 있다...
시이(swi)는 하라는 공부는 안하고 연애만 하는 학생들이 NLCS Jeju에 너무 많은 것을 보고 이들에게 시이-빔을 쏘아 단죄하기로 하였다.
언제나처럼 화재경보기가 오작동해 학생 $N$명이 대피하여 운동장에 한 줄로 서있다. 시이는 커플인 두 사람 중 한 명 이상을 단죄하려고 한다. 하지만 이들 중 누가 커플인지 모르기 때문에 시이는 다음 규칙에 따라 학생들을 단죄하기로 하였다.
- 모든 서로 인접한 두 학생 중 한 명 이상을 단죄해야 한다.
하지만 각 학생은 시이-빔에 대한 저항력이 있어 앞에서 $i$번째 학생을 시이-빔으로 단죄하기 위해서는 $R_i$만큼의 에너지가 필요하다.
이러한 시이의 행동에 분노한 학생들은 몇 명의 머리를 대머리로 만들어 시이-빔을 반사하려 한다. 대머리인 학생에게 시이-빔을 쏘면 대머리에 반사되어 시이가 공격을 입게 된다. 따라서 시이는 대머리가 아닌 학생에게만 시이-빔을 쏠 수 있다. 하지만 이웃한 두 학생을 모두 대머리로 만들면 미관상 단죄당하느니만 못하므로 이웃한 두 명의 학생을 모두 대머리로 만들 수 없다.
학생들은 일부 인원을 적절히 대머리로 만들어 시이가 단죄에 성공하기 위해 필요한 최소 에너지를 최대화하려고 한다. 학생들이 대머리가 되어 시이가 단죄하는 데 필요한 에너지가 최대일 때 얼마나 많은 에너지가 필요한지 구해 보자.
출력
학생들이 대머리가 되어 시이가 소모해야 하는 최소 에너지가 최대가 되었을 때 시이가 소모해야 하는 총 에너지를 정수로 출력한다.
제한
- 1ドル \le N \le 100,000円$
- 1ドル \le R_i \le 10^9$
- 학생들의 머리를 밀기 전에 대머리인 학생은 존재하지 않는다.
첫 번째, 네 번째 학생을 대머리로 만드는 것이 최적이다.
[{"problem_id":"31675","problem_lang":"0","title":"\ud2b9\ubcc4\ud55c \ubb3c\ub9ac \uacf5\uaca9","description":"<blockquote>\r\n<p>NLCS Jeju\uc5d0\ub294 \ud654\uc7ac \uacbd\ubcf4\uac00 \uc6b8\ub9ac\uba74 \ubaa8\ub4e0 \ucee4\ud50c\uc774 \ud5e4\uc5b4\uc9c4\ub2e4\ub294 \uc9d5\ud06c\uc2a4\uac00 \uc788\ub2e4...<\/p>\r\n<\/blockquote>\r\n\r\n<p>\uc2dc\uc774(swi)\ub294 \ud558\ub77c\ub294 \uacf5\ubd80\ub294 \uc548\ud558\uace0 \uc5f0\uc560\ub9cc \ud558\ub294 \ud559\uc0dd\ub4e4\uc774 NLCS Jeju\uc5d0 \ub108\ubb34 \ub9ce\uc740 \uac83\uc744 \ubcf4\uace0 \uc774\ub4e4\uc5d0\uac8c \uc2dc\uc774-\ube54\uc744 \uc3d8\uc544 \ub2e8\uc8c4\ud558\uae30\ub85c \ud558\uc600\ub2e4.<\/p>\r\n\r\n<p>\uc5b8\uc81c\ub098\ucc98\ub7fc \ud654\uc7ac\uacbd\ubcf4\uae30\uac00 \uc624\uc791\ub3d9\ud574 \ud559\uc0dd $N$\uba85\uc774 \ub300\ud53c\ud558\uc5ec \uc6b4\ub3d9\uc7a5\uc5d0 \ud55c \uc904\ub85c \uc11c\uc788\ub2e4. \uc2dc\uc774\ub294 \ucee4\ud50c\uc778 \ub450 \uc0ac\ub78c \uc911 \ud55c \uba85 \uc774\uc0c1\uc744 \ub2e8\uc8c4\ud558\ub824\uace0 \ud55c\ub2e4. \ud558\uc9c0\ub9cc \uc774\ub4e4 \uc911 \ub204\uac00 \ucee4\ud50c\uc778\uc9c0 \ubaa8\ub974\uae30 \ub54c\ubb38\uc5d0 \uc2dc\uc774\ub294 \ub2e4\uc74c \uaddc\uce59\uc5d0 \ub530\ub77c \ud559\uc0dd\ub4e4\uc744 \ub2e8\uc8c4\ud558\uae30\ub85c \ud558\uc600\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\ubaa8\ub4e0 \uc11c\ub85c \uc778\uc811\ud55c \ub450 \ud559\uc0dd \uc911 \ud55c \uba85 \uc774\uc0c1\uc744 \ub2e8\uc8c4\ud574\uc57c \ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\ud558\uc9c0\ub9cc \uac01 \ud559\uc0dd\uc740 \uc2dc\uc774-\ube54\uc5d0 \ub300\ud55c \uc800\ud56d\ub825\uc774 \uc788\uc5b4 \uc55e\uc5d0\uc11c $i$\ubc88\uc9f8 \ud559\uc0dd\uc744 \uc2dc\uc774-\ube54\uc73c\ub85c \ub2e8\uc8c4\ud558\uae30 \uc704\ud574\uc11c\ub294 $R_i$\ub9cc\ud07c\uc758 \uc5d0\ub108\uc9c0\uac00 \ud544\uc694\ud558\ub2e4.<\/p>\r\n\r\n<p>\uc774\ub7ec\ud55c \uc2dc\uc774\uc758 \ud589\ub3d9\uc5d0 \ubd84\ub178\ud55c \ud559\uc0dd\ub4e4\uc740 \uba87 \uba85\uc758 \uba38\ub9ac\ub97c \ub300\uba38\ub9ac\ub85c \ub9cc\ub4e4\uc5b4 \uc2dc\uc774-\ube54\uc744 \ubc18\uc0ac\ud558\ub824 \ud55c\ub2e4. \ub300\uba38\ub9ac\uc778 \ud559\uc0dd\uc5d0\uac8c \uc2dc\uc774-\ube54\uc744 \uc3d8\uba74 \ub300\uba38\ub9ac\uc5d0 \ubc18\uc0ac\ub418\uc5b4 \uc2dc\uc774\uac00 \uacf5\uaca9\uc744 \uc785\uac8c \ub41c\ub2e4. \ub530\ub77c\uc11c \uc2dc\uc774\ub294 \ub300\uba38\ub9ac\uac00 \uc544\ub2cc \ud559\uc0dd\uc5d0\uac8c\ub9cc \uc2dc\uc774-\ube54\uc744 \uc3e0 \uc218 \uc788\ub2e4. \ud558\uc9c0\ub9cc \uc774\uc6c3\ud55c \ub450 \ud559\uc0dd\uc744 \ubaa8\ub450 \ub300\uba38\ub9ac\ub85c \ub9cc\ub4e4\uba74 \ubbf8\uad00\uc0c1 \ub2e8\uc8c4\ub2f9\ud558\ub290\ub2c8\ub9cc \ubabb\ud558\ubbc0\ub85c \uc774\uc6c3\ud55c \ub450 \uba85\uc758 \ud559\uc0dd\uc744 \ubaa8\ub450 \ub300\uba38\ub9ac\ub85c \ub9cc\ub4e4 \uc218 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\ud559\uc0dd\ub4e4\uc740 \uc77c\ubd80 \uc778\uc6d0\uc744 \uc801\uc808\ud788 \ub300\uba38\ub9ac\ub85c \ub9cc\ub4e4\uc5b4 \uc2dc\uc774\uac00 \ub2e8\uc8c4\uc5d0 \uc131\uacf5\ud558\uae30 \uc704\ud574 \ud544\uc694\ud55c \ucd5c\uc18c \uc5d0\ub108\uc9c0\ub97c \ucd5c\ub300\ud654\ud558\ub824\uace0 \ud55c\ub2e4. \ud559\uc0dd\ub4e4\uc774 \ub300\uba38\ub9ac\uac00 \ub418\uc5b4 \uc2dc\uc774\uac00 \ub2e8\uc8c4\ud558\ub294 \ub370 \ud544\uc694\ud55c \uc5d0\ub108\uc9c0\uac00 \ucd5c\ub300\uc77c \ub54c \uc5bc\ub9c8\ub098 \ub9ce\uc740 \uc5d0\ub108\uc9c0\uac00 \ud544\uc694\ud55c\uc9c0 \uad6c\ud574 \ubcf4\uc790.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \ud559\uc0dd\uc758 \uc218\ub97c \ub098\ud0c0\ub0b4\ub294 \uc815\uc218 $N$\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\uc5d0 \uac01 \ud559\uc0dd\uc758 \uc800\ud56d\ub825\uc744 \ub098\ud0c0\ub0b4\ub294 \uc815\uc218 $R_i$\uac00 \uacf5\ubc31\uc744 \uc0ac\uc774\uc5d0 \ub450\uace0 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\ud559\uc0dd\ub4e4\uc774 \ub300\uba38\ub9ac\uac00 \ub418\uc5b4 \uc2dc\uc774\uac00 \uc18c\ubaa8\ud574\uc57c \ud558\ub294 \ucd5c\uc18c \uc5d0\ub108\uc9c0\uac00 \ucd5c\ub300\uac00 \ub418\uc5c8\uc744 \ub54c \uc2dc\uc774\uac00 \uc18c\ubaa8\ud574\uc57c \ud558\ub294 \ucd1d \uc5d0\ub108\uc9c0\ub97c \uc815\uc218\ub85c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>$1 \\le N \\le 100\\,000$<\/li>\r\n\t<li>$1 \\le R_i \\le 10^9$<\/li>\r\n\t<li>\ud559\uc0dd\ub4e4\uc758 \uba38\ub9ac\ub97c \ubc00\uae30 \uc804\uc5d0 \ub300\uba38\ub9ac\uc778 \ud559\uc0dd\uc740 \uc874\uc7ac\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/li>\r\n<\/ul>\r\n","sample_explain_1":"<p>\uccab \ubc88\uc9f8, \ub124 \ubc88\uc9f8 \ud559\uc0dd\uc744 \ub300\uba38\ub9ac\ub85c \ub9cc\ub4dc\ub294 \uac83\uc774 \ucd5c\uc801\uc774\ub2e4.<\/p>\r\n"},{"problem_id":"31675","problem_lang":"1","title":"Exceptional Physical Attack","description":"<blockquote>\r\n<p>There is a weird jinx in NLCS Jeju that couples break up whenever there is a fire alarm.<\/p>\r\n<\/blockquote>\r\n\r\n<p>Swi decided to shoot a Swi-beam to purge students who were dating other students instead of studying.<\/p>\r\n\r\n<p>As always, a false alarm happened. Thus, $N$ students evacuated and formed a line on the astroturf. Swi will purge at least one person out of each couple. However, since she does not know who has a boyfriend\/girlfriend, she decided to purge students based on the following criterion.<\/p>\r\n\r\n<ul>\r\n\t<li>Swi needs to purge at least one person out of all pairs of adjacent students.<\/li>\r\n<\/ul>\r\n\r\n<p>However, each student has a certain amount of resistance to the Swi-beam. Therefore, she needs $R_i$ of energy to purge the student who comes $i$-th from the front.<\/p>\r\n\r\n<p>Students, annoyed by Swi, will reflect Swi-beam by shaving some of the students&#39; hair. Since bald students will reflect Swi-beams, Swi cannot shoot Swi-beams to them. However, making two adjacent students bald is even worse than purging them due to aesthetic reasons, so students cannot shave both of two adjacent students&#39; hair.<\/p>\r\n\r\n<p>Students will appropriately shave some students&#39; hair to maximise the amount of energy Swi needs to successfully purge couples. Find the energy required for Swi to purge the students when the energy required to do so is maximum due to students shaving.<\/p>\r\n","input":"<p>The first line contains a single integer&nbsp;$N$ $-$ the number of students.<\/p>\r\n\r\n<p>The second line contains $N$ integers $R_i$ $-$ the $i$-th&nbsp;student&#39;s&nbsp;resistance.<\/p>\r\n","output":"<p>Print a single integer&nbsp;$-$ the&nbsp;total energy that Swi will need&nbsp;when the students shave their heads and the minimum energy that Swi needs is at the&nbsp;maximum.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>$1 \\le N \\le 100\\,000$<\/li>\r\n\t<li>$1 \\le R_i \\le 10^9$<\/li>\r\n\t<li>No student is bald before shaving their head.<\/li>\r\n<\/ul>\r\n","sample_explain_1":"<p>It is optimal to bald the first and fourth student.<\/p>\r\n"}]