시간 제한메모리 제한제출정답맞은 사람정답 비율
1 초 (추가 시간 없음) 1024 MB107534053.333%

문제

무한히 넓은 당근 밭 가운데 $x$, $y$ 축으로 수평인 직사각형 마구간이 있다. 그림 B.1 의 왼쪽 그림처럼 마구간의 왼쪽 아래 모서리 기둥에 말이 묶여 있고, 마구간의 네 모서리는 모두 격자점에 있다. 상하좌우로 인접한 두 격자점 사이의 간격은 $1$이다. 말을 묶은 줄의 길이는 $L$로 유한하다. 그리고 당근 밭의 모든 격자점마다 하나씩 당근이 심어져 있다. 그리고 말을 묶은 줄이 닿을 수 있는 거리 안에 심어진 당근은 말이 모두 먹을 수 있다고 가정한다.

만일 마구간의 크기가 11 × 6이고 묶은 줄의 길이가 9일때, 말이 먹을 수 있는 당근이 그림 B.1 의 오른쪽 그림에서 점으로 표시되어 있다. 단, 말과 말을 묶은 줄은 마굿간안으로는 들어갈 수 없으며 마굿간의 경계와 내부에는 당근이 심어져 있지 않다.

그림 B.1 (왼쪽) 마구간과 길이 9 인 줄에 묶인 말. (오른쪽) 말이 먹을 수 있는 모든 당근 (점).

마구간의 크기 $w \times h$ 와 말을 묶은 줄의 길이 $L$, 이렇게 3 개의 정수 $w$, $h$, $L$ 이 주어졌을 때, 말이 먹을 수 있는 당근의 최대 개수를 구하는 프로그램을 작성하시오. 격자점과 말을 묶은 기둥과의 거리가 정확하게 $L$인 경우, 이 격자점의 당근은 말이 먹을 수 있음에 유의하자.

입력

입력은 표준입력을 사용한다. 첫 번째 줄에 마구간의 크기와 줄의 길이를 나타내는 3 개의 양의 정수 $w$, $h$, $L$ ($1 \le w, h, L \le 100,000$)가 주어진다.

출력

출력은 표준출력을 사용한다. 주어진 조건에서 말이 먹을 수 있는 당근의 최대 개수를 첫 번째 줄에 정수로 출력한다.

예제 입력 1

11 6 3

예제 출력 1

18

그림 B.2 첫 번째 테스트 케이스에 대한 설명

예제 입력 2

11 6 15

예제 출력 2

591

예제 입력 3

11 6 20

예제 출력 3

1134
[{"problem_id":"23239","problem_lang":"0","title":"\ub2f9\uadfc \ubc2d","description":"<p>\ubb34\ud55c\ud788 \ub113\uc740 \ub2f9\uadfc \ubc2d \uac00\uc6b4\ub370 $x$, $y$ \ucd95\uc73c\ub85c \uc218\ud3c9\uc778 \uc9c1\uc0ac\uac01\ud615 \ub9c8\uad6c\uac04\uc774 \uc788\ub2e4. \uadf8\ub9bc B.1 \uc758 \uc67c\ucabd \uadf8\ub9bc\ucc98\ub7fc \ub9c8\uad6c\uac04\uc758 \uc67c\ucabd \uc544\ub798 \ubaa8\uc11c\ub9ac \uae30\ub465\uc5d0 \ub9d0\uc774 \ubb36\uc5ec \uc788\uace0, \ub9c8\uad6c\uac04\uc758 \ub124 \ubaa8\uc11c\ub9ac\ub294 \ubaa8\ub450 \uaca9\uc790\uc810\uc5d0 \uc788\ub2e4. \uc0c1\ud558\uc88c\uc6b0\ub85c \uc778\uc811\ud55c \ub450 \uaca9\uc790\uc810 \uc0ac\uc774\uc758 \uac04\uaca9\uc740 $1$\uc774\ub2e4. \ub9d0\uc744 \ubb36\uc740 \uc904\uc758 \uae38\uc774\ub294 $L$\ub85c \uc720\ud55c\ud558\ub2e4. \uadf8\ub9ac\uace0 \ub2f9\uadfc \ubc2d\uc758 \ubaa8\ub4e0 \uaca9\uc790\uc810\ub9c8\ub2e4 \ud558\ub098\uc529 \ub2f9\uadfc\uc774 \uc2ec\uc5b4\uc838 \uc788\ub2e4. \uadf8\ub9ac\uace0 \ub9d0\uc744 \ubb36\uc740 \uc904\uc774 \ub2ff\uc744 \uc218 \uc788\ub294 \uac70\ub9ac \uc548\uc5d0 \uc2ec\uc5b4\uc9c4 \ub2f9\uadfc\uc740 \ub9d0\uc774 \ubaa8\ub450 \uba39\uc744 \uc218 \uc788\ub2e4\uace0 \uac00\uc815\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub9cc\uc77c \ub9c8\uad6c\uac04\uc758 \ud06c\uae30\uac00 11 &times;&nbsp;6\uc774\uace0 \ubb36\uc740 \uc904\uc758 \uae38\uc774\uac00 9\uc77c\ub54c, \ub9d0\uc774 \uba39\uc744 \uc218 \uc788\ub294 \ub2f9\uadfc\uc774 \uadf8\ub9bc B.1 \uc758 \uc624\ub978\ucabd \uadf8\ub9bc\uc5d0\uc11c \uc810\uc73c\ub85c \ud45c\uc2dc\ub418\uc5b4 \uc788\ub2e4. \ub2e8, \ub9d0\uacfc \ub9d0\uc744 \ubb36\uc740 \uc904\uc740 \ub9c8\uad7f\uac04\uc548\uc73c\ub85c\ub294 \ub4e4\uc5b4\uac08 \uc218 \uc5c6\uc73c\uba70 \ub9c8\uad7f\uac04\uc758 \uacbd\uacc4\uc640 \ub0b4\ubd80\uc5d0\ub294 \ub2f9\uadfc\uc774 \uc2ec\uc5b4\uc838 \uc788\uc9c0 \uc54a\ub2e4.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/615e851b-5658-4de7-878a-d050e06cc9bc\/-\/preview\/\" style=\"width: 549px; height: 240px;\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">\uadf8\ub9bc B.1 (\uc67c\ucabd) \ub9c8\uad6c\uac04\uacfc \uae38\uc774 9 \uc778 \uc904\uc5d0 \ubb36\uc778 \ub9d0. (\uc624\ub978\ucabd) \ub9d0\uc774 \uba39\uc744 \uc218 \uc788\ub294 \ubaa8\ub4e0 \ub2f9\uadfc (\uc810).<\/p>\r\n\r\n<p>\ub9c8\uad6c\uac04\uc758 \ud06c\uae30 $w&nbsp;\\times h$ \uc640 \ub9d0\uc744 \ubb36\uc740 \uc904\uc758 \uae38\uc774 $L$, \uc774\ub807\uac8c 3 \uac1c\uc758 \uc815\uc218 $w$, $h$, $L$ \uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ub9d0\uc774 \uba39\uc744 \uc218 \uc788\ub294 \ub2f9\uadfc\uc758 \ucd5c\ub300 \uac1c\uc218\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624. \uaca9\uc790\uc810\uacfc \ub9d0\uc744 \ubb36\uc740 \uae30\ub465\uacfc\uc758 \uac70\ub9ac\uac00 \uc815\ud655\ud558\uac8c $L$\uc778 \uacbd\uc6b0, \uc774 \uaca9\uc790\uc810\uc758 \ub2f9\uadfc\uc740 \ub9d0\uc774 \uba39\uc744 \uc218 \uc788\uc74c\uc5d0 \uc720\uc758\ud558\uc790.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \ud45c\uc900\uc785\ub825\uc744 \uc0ac\uc6a9\ud55c\ub2e4. \uccab \ubc88\uc9f8 \uc904\uc5d0 \ub9c8\uad6c\uac04\uc758 \ud06c\uae30\uc640 \uc904\uc758 \uae38\uc774\ub97c \ub098\ud0c0\ub0b4\ub294 3 \uac1c\uc758 \uc591\uc758 \uc815\uc218 $w$, $h$, $L$ ($1 \\le w, h, L \\le 100,000$)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\ucd9c\ub825\uc740 \ud45c\uc900\ucd9c\ub825\uc744 \uc0ac\uc6a9\ud55c\ub2e4. \uc8fc\uc5b4\uc9c4 \uc870\uac74\uc5d0\uc11c \ub9d0\uc774 \uba39\uc744 \uc218 \uc788\ub294 \ub2f9\uadfc\uc758 \ucd5c\ub300 \uac1c\uc218\ub97c \uccab \ubc88\uc9f8 \uc904\uc5d0 \uc815\uc218\ub85c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","sample_explain_1":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/e3e177d5-b805-4bda-808e-d99db542bb44\/-\/preview\/\" style=\"width: 318px; height: 240px;\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">\uadf8\ub9bc B.2 \uccab \ubc88\uc9f8 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud55c \uc124\uba85<\/p>\r\n"},{"problem_id":"23239","problem_lang":"1","title":"Carrot Field","description":"<p>In the middle of an infinitely wide carrot field, there is a rectangular stable whose sides are parallel either to $x$-axis or to $y$-axis. Each corner of the stable has integer coordinates. A horse is tied to a pole in the lower left corner of the stable as shown in Figure B.1. The length of the leash tied to this horse is $L$. A carrot is planted for every two-dimensional grid point in the carrot field, and the horse can eat any carrot planted within the reach of the leash.<\/p>\r\n\r\n<p>For example, if the size of the stable is 11 &times; 6 and the length of the leash is 9, the carrots that the horse can eat are indicated by the dots in the right of Figure B.1 below. But note that the horse and the leash cannot enter the stable, and there are no carrots planted on the sides and the interior of the stable.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/615e851b-5658-4de7-878a-d050e06cc9bc\/-\/preview\/\" style=\"width: 549px; height: 240px;\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">Figure B.1 The horse is tied to the lower left corner of the stable by the leash of length 9 (left). Dots represent the carrots that the horse can eat (right).<\/p>\r\n\r\n<p>You are given three integers $w$, $h$, and $L$ where the stable has width $w$ and height $h$, and the leash has length $L$. Write a program to compute the maximum number of carrots a horse can eat. Note that if the distance between a grid point and the corner to which the horse is tied is exactly $L$, the horse can eat the carrot at the grid point.<\/p>\r\n","input":"<p>Your program is to read from standard input. The first line contains three positive integers $w$, $h$, and $L$ ($1 \\le w, h, L \\le 100,000$) where $w$ and $h$ represent the width and the height of the stable, respectively, and $L$ is the length of the leash.<\/p>\r\n","output":"<p>Your program is to write to standard output. Print exactly one line which contains the maximum number of carrots a horse can eat.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","sample_explain_1":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/e3e177d5-b805-4bda-808e-d99db542bb44\/-\/preview\/\" style=\"width: 318px; height: 240px;\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">Figure B.2 The illustration for the first sample test case.<\/p>\r\n"}]