시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 1398 548 388 39.152%

문제

상근이는 사탕에 중독된 아이이다. 상근이는 캔디 매거진의 열렬한 구독자이며, 올해 열리는 국제 사탕 줍기 대회에 한국 대표로 참가하게 되었다.

이 대회는 사탕을 포함하고 있는 박스가 M행 N열로 놓여져있는 곳에서 진행된다. (따라서 박스는 총 M × N개 있다) 각 박스에는 들어있는 사탕의 개수가 겉에 적혀져 있다.

대회의 참가자는 박스를 하나 고른다. 그 다음, 그 박스 안에 있는 사탕을 모두 가져가게 된다. 박스를 고르면, 고른 박스의 바로 위쪽 행과 바로 아래쪽 행에 있는 모든 박스, 그리고 고른 박스의 왼쪽과 오른쪽에 있는 박스에 들어있는 사탕이 모두 사라지게 된다. 참가자는 사탕이 들어있는 박스가 없을 때까지 박스를 고를 수 있다.

아래 그림을 살펴보자. 각 칸은 박스에 들어있는 사탕의 개수를 나타낸다. 각각의 단계에서 참가자가 고른 박스는 동그라미로 표시되어 있고, 회색으로 칠해진 박스는 참가자의 선택 때문에 사탕이 사라질 박스이다. 총 여덟 단계가 지나면 게임은 끝나게 되고, 상근이는 총 10+9+8+3+7+6+10+1 = 54개의 사탕을 가져가게 된다.

M과 N이 주어졌을 때, 상근이가 이 대회에서 가져갈 수 있는 사탕의 최대 개수를 구하는 프로그램을 작성하시오. 

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다. 각 테스트 케이스의 첫째 줄에는 M과 N이 주어졌다. (1 ≤ M × N ≤ 105) 다음 M개 줄에는 박스에 들어있는 사탕의 개수 N개가 주어진다. 박스에 들어있는 사탕은 적어도 1개이며 103개를 넘지 않는다.

입력의 마지막 줄에는 0이 두 개 주어진다.

출력

각 테스트 케이스에 대해 상근이가 집을 수 있는 사탕의 최대 개수를 출력한다.

예제 입력 1

5 5
1 8 2 1 9
1 7 3 5 2
1 2 10 3 10
8 4 7 9 1
7 1 3 1 6
4 4
10 1 1 10
1 1 1 1
1 1 1 1
10 1 1 10
2 4
9 10 2 7
5 1 1 5
0 0

예제 출력 1

54
40
17
[{"problem_id":"5721","problem_lang":"0","title":"\uc0ac\ud0d5 \uc90d\uae30 \ub300\ud68c","description":"<p>\uc0c1\uadfc\uc774\ub294 \uc0ac\ud0d5\uc5d0 \uc911\ub3c5\ub41c \uc544\uc774\uc774\ub2e4. \uc0c1\uadfc\uc774\ub294 \uce94\ub514 \ub9e4\uac70\uc9c4\uc758 \uc5f4\ub82c\ud55c \uad6c\ub3c5\uc790\uc774\uba70, \uc62c\ud574 \uc5f4\ub9ac\ub294 \uad6d\uc81c \uc0ac\ud0d5 \uc90d\uae30 \ub300\ud68c\uc5d0 \ud55c\uad6d \ub300\ud45c\ub85c \ucc38\uac00\ud558\uac8c \ub418\uc5c8\ub2e4.<\/p>\r\n\r\n<p>\uc774 \ub300\ud68c\ub294 \uc0ac\ud0d5\uc744 \ud3ec\ud568\ud558\uace0 \uc788\ub294 \ubc15\uc2a4\uac00 M\ud589&nbsp;N\uc5f4\ub85c \ub193\uc5ec\uc838\uc788\ub294 \uacf3\uc5d0\uc11c \uc9c4\ud589\ub41c\ub2e4. (\ub530\ub77c\uc11c \ubc15\uc2a4\ub294 \ucd1d M &times; N\uac1c \uc788\ub2e4) \uac01 \ubc15\uc2a4\uc5d0\ub294 \ub4e4\uc5b4\uc788\ub294 \uc0ac\ud0d5\uc758 \uac1c\uc218\uac00 \uac89\uc5d0 \uc801\ud600\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ub300\ud68c\uc758 \ucc38\uac00\uc790\ub294 \ubc15\uc2a4\ub97c \ud558\ub098 \uace0\ub978\ub2e4. \uadf8 \ub2e4\uc74c, \uadf8 \ubc15\uc2a4 \uc548\uc5d0 \uc788\ub294 \uc0ac\ud0d5\uc744 \ubaa8\ub450 \uac00\uc838\uac00\uac8c \ub41c\ub2e4. \ubc15\uc2a4\ub97c \uace0\ub974\uba74, \uace0\ub978 \ubc15\uc2a4\uc758 \ubc14\ub85c \uc704\ucabd \ud589\uacfc \ubc14\ub85c \uc544\ub798\ucabd \ud589\uc5d0 \uc788\ub294 \ubaa8\ub4e0 \ubc15\uc2a4, \uadf8\ub9ac\uace0 \uace0\ub978 \ubc15\uc2a4\uc758 \uc67c\ucabd\uacfc \uc624\ub978\ucabd\uc5d0 \uc788\ub294 \ubc15\uc2a4\uc5d0 \ub4e4\uc5b4\uc788\ub294 \uc0ac\ud0d5\uc774 \ubaa8\ub450 \uc0ac\ub77c\uc9c0\uac8c \ub41c\ub2e4. \ucc38\uac00\uc790\ub294 \uc0ac\ud0d5\uc774 \ub4e4\uc5b4\uc788\ub294 \ubc15\uc2a4\uac00 \uc5c6\uc744 \ub54c\uae4c\uc9c0 \ubc15\uc2a4\ub97c \uace0\ub97c \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc544\ub798 \uadf8\ub9bc\uc744 \uc0b4\ud3b4\ubcf4\uc790. \uac01 \uce78\uc740 \ubc15\uc2a4\uc5d0 \ub4e4\uc5b4\uc788\ub294 \uc0ac\ud0d5\uc758 \uac1c\uc218\ub97c \ub098\ud0c0\ub0b8\ub2e4. \uac01\uac01\uc758 \ub2e8\uacc4\uc5d0\uc11c \ucc38\uac00\uc790\uac00 \uace0\ub978 \ubc15\uc2a4\ub294 \ub3d9\uadf8\ub77c\ubbf8\ub85c \ud45c\uc2dc\ub418\uc5b4 \uc788\uace0, \ud68c\uc0c9\uc73c\ub85c \uce60\ud574\uc9c4 \ubc15\uc2a4\ub294 \ucc38\uac00\uc790\uc758 \uc120\ud0dd \ub54c\ubb38\uc5d0 \uc0ac\ud0d5\uc774 \uc0ac\ub77c\uc9c8 \ubc15\uc2a4\uc774\ub2e4. \ucd1d \uc5ec\ub35f \ub2e8\uacc4\uac00 \uc9c0\ub098\uba74 \uac8c\uc784\uc740 \ub05d\ub098\uac8c \ub418\uace0, \uc0c1\uadfc\uc774\ub294 \ucd1d 10+9+8+3+7+6+10+1 = 54\uac1c\uc758 \uc0ac\ud0d5\uc744 \uac00\uc838\uac00\uac8c \ub41c\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/candy.png\" style=\"height:322px; width:633px\" \/><\/p>\r\n\r\n<p>M\uacfc N\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc0c1\uadfc\uc774\uac00 \uc774 \ub300\ud68c\uc5d0\uc11c \uac00\uc838\uac08 \uc218 \uc788\ub294 \uc0ac\ud0d5\uc758 \ucd5c\ub300 \uac1c\uc218\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.&nbsp;<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 M\uacfc N\uc774 \uc8fc\uc5b4\uc84c\ub2e4. (1 &le; M &times; N &le; 10<sup>5<\/sup>) \ub2e4\uc74c M\uac1c \uc904\uc5d0\ub294 \ubc15\uc2a4\uc5d0 \ub4e4\uc5b4\uc788\ub294 \uc0ac\ud0d5\uc758 \uac1c\uc218 N\uac1c\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ubc15\uc2a4\uc5d0 \ub4e4\uc5b4\uc788\ub294 \uc0ac\ud0d5\uc740 \uc801\uc5b4\ub3c4 1\uac1c\uc774\uba70 10<sup>3<\/sup>\uac1c\ub97c \ub118\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\uc785\ub825\uc758 \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 0\uc774 \ub450 \uac1c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574 \uc0c1\uadfc\uc774\uac00 \uc9d1\uc744 \uc218 \uc788\ub294 \uc0ac\ud0d5\uc758 \ucd5c\ub300 \uac1c\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"5721","problem_lang":"1","title":"Candy Distribution","description":"<p>Little Charlie is a nice boy addicted to candies. He is even a subscriber to All Candies Magazine and was selected to participate in the International Candy Picking Contest.<\/p>\r\n\r\n<p>In this contest a random number of boxes containing candies are disposed in M rows with N columns each (so, there are a total of M &times; N boxes). Each box has a number indicating how many candies it contains.<\/p>\r\n\r\n<p>The contestant can pick a box (any one) and get all the candies it contains. But there is a catch (there is always a catch): when choosing a box, all the boxes from the rows immediately above and immediately below are emptied, as well as the box to the left and the box to the right of the chosen box. The contestant continues to pick a box until there are no candies left.<\/p>\r\n\r\n<p>The \ufb01gure bellow illustrates this, step by step. Each cell represents one box and the number of candies it contains. At each step, the chosen box is circled and the shaded cells represent the boxes that will be emptied. After eight steps the game is over and Charlie picked 10 + 9 + 8 + 3 + 7 + 6 + 10 + 1 = 54 candies.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/candy.png\" style=\"height:322px; width:633px\" \/><\/p>\r\n\r\n<p>For small values of M and N, Charlie can easily \ufb01nd the maximum number of candies he can pick, but when the numbers are really large he gets completely lost. Can you help Charlie maximize the number of candies he can pick?<\/p>\r\n","input":"<p>The input contains several test cases. The \ufb01rst line of a test case contains two positive integers M and N (1 &le; M &times; N &le; 10<sup>5<\/sup>), separated by a single space, indicating the number of rows and columns respectively. Each of the following M lines contains N integers separated by single spaces, each representing the initial number of candies in the corresponding box. Each box will have initially at least 1 and at most 10<sup>3<\/sup> candies.<\/p>\r\n\r\n<p>The end of input is indicated by a line containing two zeroes separated by a single space.<\/p>\r\n","output":"<p>For each test case in the input, your program must print a single line, containing a single value, the integer indicating the maximum number of candies that Charlie can pick.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ACM-ICPC > Regionals > Latin America > South America Regional Contests 2008 C번