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문제

러시아 전통 목제인형인 마트료시카는 그 안에 크기가 계속 작아지는 인형들이 들어있는 인형이다. 마트료시카를 열면 그 안에 더 작은 인형이 있고, 그 작은 인형의 안엔 또다시 작은 인형이 들어있고, 안에 더는 인형이 없을 때까지 계속 반복된다. 

최근 러시아 마트료시카 박물관은 개수만 다르고 비슷하게 생긴 마트료시카 세트들을 모아놓은 콜렉션을 전시했다. 그런데 그만부모의 통제에서 벗어난 난폭한 어린이들이 이 세트들을 모두 분리시켜 일렬로 세워버렸다. 박물관 알바생인 준빈이는 해고 당하지 않기 위해 어린이들이 일렬로 세워놓은 총 n개의 마트료시카를(인형들의 크기는 정수로 나타낼 수 있다고 가정하자), 원래 마트료시카 세트들이 몇 개였는지 세트별로 몇 개였는지 모르는 채로, 마트료시카 세트들로 재조립 해야 한다. 확실한 것은 모든 완전한 마트료시카 세트의 인형들의 크기들은 각각 크기가 1부터 어떤 수 m까지의 연속된 정수라는 것이다. 물론 m은 각 세트마다 다르다.

재조립 과정에서 준빈이는 다음의 규칙을 따라야한다.

  • 작은 인형 안에는 큰 인형이 들어갈 수 없다.
  • 두 그룹(부분적으로 재조립이 완료된 그룹)의 인형들을 합치려면 그 두 그룹이 (줄에서)서로 인접해 있어야 한다.
  • 인형이 한 번 그룹에 들어가면 다른 그룹과 합치는 작업을 할 때 외에는, 절대로 다른 그룹으로 옮기거나 아예 분리될 수 없다.

오래 걸리면 걸릴 수록 시급에서 까인다. 따라서 최대한 빨리 이 일을 마쳐야 한다. 복구할 때 인형을 열고 닫는 시간만 고려하자. 따라서 여는 횟수를 최소화하면 된다.  예를 들어보자. 그룹 [1, 2, 6]과 [4]를 합칠 때 여는 횟수의 최솟값은 2이다. 크기 6인 인형과 4인 인형을 열어야 하기 때문이다. 그룹 [1, 2, 5]와 [3, 4]를 합칠 때는 최소 횟수가 3이다.

분해된 마트료시카 세트들을 다시 합치는데 인형들을 최소 몇 번 열어야하는지 계산하자.

입력

첫 번째 줄에는 일렬로 세워진 각 마트료시카 인형들의 개수 n(1 ≤ n ≤ 500)이 주어진다. 두 번째 줄에는 각 마트료시카 인형의 크기(1 ≤ 크기 ≤ 500)가 줄에 세워진 순서대로 주어진다.

출력

마트료시카 세트들을 복구하기 위해 인형들을 여는 횟수의 최솟값을 출력한다. 만약 재조립이 불가능하다면(아이들이 훔쳤을 수도 있다) "impossible"을 출력한다.

예제 입력 1

7
1 2 3 2 4 1 3

예제 출력 1

7
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n &le; 500)\uc774&nbsp;\uc8fc\uc5b4\uc9c4\ub2e4. \ub450 \ubc88\uc9f8 \uc904\uc5d0\ub294 \uac01 \ub9c8\ud2b8\ub8cc\uc2dc\uce74 \uc778\ud615\uc758 \ud06c\uae30(1 &le; \ud06c\uae30 &le; 500)\uac00 \uc904\uc5d0 \uc138\uc6cc\uc9c4 \uc21c\uc11c\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\ub9c8\ud2b8\ub8cc\uc2dc\uce74 \uc138\ud2b8\ub4e4\uc744 \ubcf5\uad6c\ud558\uae30 \uc704\ud574 \uc778\ud615\ub4e4\uc744 \uc5ec\ub294 \ud69f\uc218\uc758 \ucd5c\uc19f\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4. \ub9cc\uc57d \uc7ac\uc870\ub9bd\uc774 \ubd88\uac00\ub2a5\ud558\ub2e4\uba74(\uc544\uc774\ub4e4\uc774 \ud6d4\ucce4\uc744 \uc218\ub3c4 \uc788\ub2e4) &quot;impossible&quot;\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"8884","problem_lang":"1","title":"\u043c\u0430\u0442\u0440\u0451\u0448\u043a\u0430","description":"<p>Matryoshkas are sets of traditional Russian wooden dolls of decreasing size placed one inside the other. A matryoshka doll can be opened to reveal a smaller \ufb01gure of the same sort inside, which has, in turn, another \ufb01gure inside, and so on.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/Matryoshka.png\" style=\"float:right; height:200px; width:261px\" \/>The Russian Matryoshka Museum recently exhibited a collection of similarly designed matryoshka sets, differing only in the number of nested dolls in each set. Unfortunately, some over-zealous (and obviously unsupervised) children separated these sets, placing all the individual dolls in a row. There are n dolls in the row, each with an integer size. You need to reassemble the matryoshka sets, knowing neither the number of sets nor the number of dolls in each set. You know only that every complete set consists of dolls with consecutive sizes from 1 to some number m, which may vary between the different sets.<\/p>\r\n\r\n<p>When reassembling the sets, you must follow these rules:<\/p>\r\n\r\n<ul>\r\n\t<li>You can put a doll or a nested group of dolls only inside a larger doll.<\/li>\r\n\t<li>You can combine two groups of dolls only if they are adjacent in the row.<\/li>\r\n\t<li>Once a doll becomes a member of a group, it cannot be transferred to another group or permanently separated from the group. It can be temporarily separated only when combining two groups.<\/li>\r\n<\/ul>\r\n\r\n<p>Your time is valuable, and you want to do this reassembly process as quickly as possible. The only time-consuming part of this task is opening and subsequently closing a doll, so you want to minimize how often you do this. For example, the minimum number of openings (and subsequent closings) when combining group [1, 2, 6] with the group [4] is two, since you have to open the dolls with sizes 6 and 4. When combining group [1, 2, 5] with the group [3, 4], you need to perform three openings.<\/p>\r\n\r\n<p>Write a program to calculate the minimum number of openings required to combine all disassembled matryoshka sets.<\/p>\r\n","input":"<p>The input consists of a single test case. A test case consists of two lines. The \ufb01rst line contains one integer n (1 &le; n &le; 500) representing the number of individual dolls in the row. The second line contains n positive integers specifying the sizes of the dolls in the order they appear in the row. Each size is between 1 and 500 inclusive.<\/p>\r\n","output":"<p>Display the minimum number of openings required when reassembling the matryoshka sets. If reassembling cannot be done (some of the kids might have been excessively zealous and taken some dolls), display the word impossible.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ACM-ICPC > World Finals > 2013 World Finals H번