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문제

윤형이와 동혁이가 블록 쌓기 놀이를 한다. 두 명 모두 너비 N의 블록 건물을 쌓았는데, 윤형이는 k번째 열에 Yk개의 블록을 쌓았고 동혁이는 k번째 열에 Dk개의 블록을 쌓았다. 윤형이와 동혁이는 블록을 쌓거나 빼면서 두 개의 똑같은 건물을 만들려고 한다.

한편, 이 둘이 새로 만들려는 건물은 위 그림의 오른쪽 형태와 같이 팩맨 모양이 되어야 한다. 즉, 왼쪽에서 오른쪽으로 갈수록 블록의 개수가 감소하다가 증가하는 꼴이 되어야 한다. 또, 인접한 두 열의 블록의 개수는 정확히 한 개씩만 차이나야 하며, 블록의 개수가 가장 적은 열은 정중앙이여야 한다.

방을 어지르지 않기 위해서, 블록을 하나 뺐으면 바로 블록 상자에 넣는다. 블록을 다른 곳으로 옮겨야 한다면, 블록을 상자에 넣었다가 빼서 원하는 곳에 쌓아야 한다. 블록 상자에는 무한히 많은 블록이 있다.

윤형이와 동혁이가 원하는 방법으로 블록 건물을 바꿀 때, 블록을 빼거나 쌓는 횟수를 최소화하는 프로그램을 작성하여라.

입력

첫 번째 줄에는 두 블록 건물의 너비 N이 주어진다. N은 홀수이다.

두 번째 줄에는 윤형이의 블록 건물의 높이 Yk가 주어진다.

세 번째 줄에는 동혁이의 블록 건물의 높이 Dk가 주어진다.

출력

블록을 쌓거나 빼는 작업의 수의 최솟값을 출력한다.

제한

  • 1 ≤ N ≤ 300,000
  • 0 ≤ Yk, Dk ≤ 1012

예제 입력 1

3
1 2 3
3 2 2

예제 출력 1

3

예제 입력 2

5
2 3 0 1 4
3 3 2 3 1

예제 출력 2

10

힌트

첫 번째 예제의 경우 윤형이의 블록 건물의 1번째 열에 블록 2개를 더 쌓고, 동혁이의 블록 건물의 3번째 열에 블록 1개를 더 쌓으면 된다.

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N\uc740 \ud640\uc218\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\uc5d0\ub294 \uc724\ud615\uc774\uc758 \ube14\ub85d \uac74\ubb3c\uc758 \ub192\uc774 Y<sub>k<\/sub>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uc138 \ubc88\uc9f8 \uc904\uc5d0\ub294 \ub3d9\ud601\uc774\uc758 \ube14\ub85d \uac74\ubb3c\uc758 \ub192\uc774 D<sub>k<\/sub>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\ube14\ub85d\uc744 \uc313\uac70\ub098 \ube7c\ub294 \uc791\uc5c5\uc758 \uc218\uc758 \ucd5c\uc19f\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\uccab \ubc88\uc9f8 \uc608\uc81c\uc758 \uacbd\uc6b0 \uc724\ud615\uc774\uc758 \ube14\ub85d \uac74\ubb3c\uc758 1\ubc88\uc9f8 \uc5f4\uc5d0 \ube14\ub85d 2\uac1c\ub97c \ub354 \uc313\uace0, \ub3d9\ud601\uc774\uc758 \ube14\ub85d \uac74\ubb3c\uc758 3\ubc88\uc9f8 \uc5f4\uc5d0 \ube14\ub85d 1\uac1c\ub97c \ub354 \uc313\uc73c\uba74 \ub41c\ub2e4.<\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>1 &le; N &le; 300,000<\/li>\r\n\t<li>0 &le; Y<sub>k<\/sub>, D<sub>k<\/sub> &le; 10<sup>12<\/sup><\/li>\r\n<\/ul>\r\n"},{"problem_id":"9998","problem_lang":"1","title":"KOCKICE","description":"<p>Mirko and Slavko are playing with bricks. Both of them have their own pile of bricks. The piles consist of N columns (where N is an odd number). The number of bricks in the i<sup>th<\/sup> column of Mirko&#39;s pile is labeled with m<sub>i<\/sub> and Slavko&#39;s pile with s<sub>i<\/sub>.&nbsp;<\/p>\r\n\r\n<p>They have decided to create two equal piles constructed in a way that the heights of columns are strictly descending at first and then strictly ascending (see right image below) and the heights of adjacent columns differ exactly by 1 (see image). The lowest of the columns must have an equalnumber of columns to the left and to the right of it.&nbsp;<\/p>\r\n\r\n<p>The piles can be modified by removing one brick from the top of some column and throw it out the window (they cannot reuse it) or by taking one brick from the box and place it on the top of some column (there is an infinite amount of bricks in the box). Removing or placing a brick counts as one move.&nbsp;<\/p>\r\n\r\n<p>You have to determine the minimal number of moves so that Mirko and Slavko can rearrange their piles in the described way.&nbsp;<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/86911055-3c2f-4e51-bce7-2a2fdcb597f3\/-\/preview\/\" style=\"width: 387px; height: 112px;\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">On the left, there is a pile with column heights 3, 2, 0, 1 and 4. On the right, there is one of the possible final layouts.<\/p>\r\n","input":"<p>The first line of input contains an odd number N. (1 &le; N &le; 300 000), the number of columns in both piles.&nbsp;<\/p>\r\n\r\n<p>The second line of input contains N integers m<sub>i<\/sub> (0 &le; m<sub>i<\/sub> &le; 10<sup>12<\/sup>), column heights in Mirko&#39;s pile.&nbsp;<\/p>\r\n\r\n<p>The third line of input contains N integers s<sub>i<\/sub> (0 &le; s<sub>i<\/sub> &le; 10<sup>12<\/sup>), column heights in Slavko&#39;s pile.&nbsp;<\/p>\r\n","output":"<p>The first and only line of output must contain the minimal number of moves.&nbsp;<\/p>\r\n","hint":"<p>Clarification of the first example: Mirko places two bricks on the top the first column in his pile and Slavko places one brick on the top of the third column in his pile.<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

Contest > Croatian Open Competition in Informatics > COCI 2013/2014 > Contest #6 3번