문제
윤이의 취미는 그림 그리기이다. 어느 날, 학교 뒷산을 보고 영감을 받은 윤이는 산수화 한 장을 그려 내었다. 산수화는 $N$행 $M$열의 격자 모양이며, 각 칸은 검은색 또는 흰색으로 칠해져 있다.
윤이는 산수화를 포닉스와 달구에게 선물하기로 했다. 그러나 그림은 한 장뿐이었고, 포닉스와 달구는 누가 그림을 가져야 하는지에 대한 토론을 시작했다. 토론은 쉽게 끝나지 않았는데 그 이유는 포닉스와 달구가 생각하는 좋은 산수화의 기준이 서로 다르기 때문이었다.
달구는 산이 많은 산수화를 좋은 산수화라고 생각하며, 포닉스는 호수가 많은 산수화를 좋은 산수화라고 생각한다. 산과 호수의 정의는 각각 아래와 같다. $(i,j)$는 $i$번째 행 $j$번째 열에 해당하는 칸을 의미한다.
- $a\le x,|a-x|+|b-y|\le d-1$를 만족하는 $(a,b)$가 모두 검은색이라면 이를 $(x,y)$를 중심으로 하고 크기가 $d$인 산이라 한다. 이때 $d$는 1ドル$ 이상 $\min(y,M-y+1,x)$ 이하의 정수여야 한다.
- $x\le a\le x+d-1,y\le b\le y+d-1$을 만족하는 $(a,b)$가 모두 흰색이라면 이를 $(x,y)$를 왼쪽 위 꼭짓점으로 하고 크기가 $d$인 호수라 한다. 이때 $d$는 1ドル$ 이상 $\min(N-x+1,M-y+1)$ 이하의 정수여야 한다.
위 그림의 경우, $(3,2)$를 중심으로 하고 크기가 2ドル$인 산과 $(1,3)$을 왼쪽 위 꼭짓점으로 하고 크기가 2ドル$인 호수가 있다.
윤이는 친구들의 토론을 멈추기 위해 1ドル$부터 $N$까지의 모든 $i$에 대해 크기가 $i$인 산의 개수와 호수의 개수를 직접 구해 주려 한다. 윤이를 도와 문제를 해결해 보자.
출력
첫째 줄에 크기가 $i$인 산의 개수를 나타내는 $N$개의 정수 $A_1, A_2, \cdots, A_N$을 공백으로 구분해 출력한다.
둘째 줄에 크기가 $i$인 호수의 개수를 나타내는 $N$개의 정수 $B_1, B_2, \cdots, B_N$을 공백으로 구분해 출력한다.
예제 출력 2
9 4 1 0 0 0
21 10 3 0 0 0
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width: 300px;\" \/><\/p>\r\n\r\n<p>\uc704 \uadf8\ub9bc\uc758 \uacbd\uc6b0, $(3,2)$\ub97c \uc911\uc2ec\uc73c\ub85c \ud558\uace0 \ud06c\uae30\uac00 $2$\uc778 \uc0b0\uacfc $(1,3)$\uc744 \uc67c\ucabd \uc704 \uaf2d\uc9d3\uc810\uc73c\ub85c \ud558\uace0 \ud06c\uae30\uac00 $2$\uc778 \ud638\uc218\uac00 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc724\uc774\ub294 \uce5c\uad6c\ub4e4\uc758 \ud1a0\ub860\uc744 \uba48\ucd94\uae30 \uc704\ud574 $1$\ubd80\ud130 $N$\uae4c\uc9c0\uc758 \ubaa8\ub4e0 $i$\uc5d0 \ub300\ud574 \ud06c\uae30\uac00 $i$\uc778 \uc0b0\uc758 \uac1c\uc218\uc640 \ud638\uc218\uc758 \uac1c\uc218\ub97c \uc9c1\uc811 \uad6c\ud574 \uc8fc\ub824 \ud55c\ub2e4. \uc724\uc774\ub97c \ub3c4\uc640 \ubb38\uc81c\ub97c \ud574\uacb0\ud574 \ubcf4\uc790.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc0b0\uc218\ud654\uc758 \ud589\uc758 \uc218 $N$\uacfc \uc5f4\uc758 \uc218 $M$\uc774 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. $(1 \\le N, M \\le 2000)$<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\ubd80\ud130 $N$\uc904\uc5d0 \uac78\uccd0 \uc0b0\uc218\ud654\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. $i+1$\ubc88\uc9f8 \uc904\uc5d0\ub294 \uc0b0\uc218\ud654\uc758 $i$\ubc88\uc9f8 \ud589\uc744 \ub098\ud0c0\ub0b4\ub294 \uae38\uc774\uac00 $M$\uc778 \ubb38\uc790\uc5f4\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ubaa8\ub4e0 \ubb38\uc790\uc5f4\uc740 <code><span style=\"color:#e74c3c;\">#<\/span><\/code> \ub610\ub294 <code><span style=\"color:#e74c3c;\">.<\/span><\/code> \uc73c\ub85c \uad6c\uc131\ub41c\ub2e4. <code><span style=\"color:#e74c3c;\">#<\/span><\/code>\uc740 \uac80\uc740\uc0c9, <code><span style=\"color:#e74c3c;\">.<\/span><\/code>\uc740 \ud770\uc0c9\uc744 \uc758\ubbf8\ud55c\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud06c\uae30\uac00 $i$\uc778 \uc0b0\uc758 \uac1c\uc218\ub97c \ub098\ud0c0\ub0b4\ub294 $N$\uac1c\uc758 \uc815\uc218 $A_1, A_2, \\cdots, A_N$\uc744 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ud574 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\uc5d0 \ud06c\uae30\uac00 $i$\uc778 \ud638\uc218\uc758 \uac1c\uc218\ub97c \ub098\ud0c0\ub0b4\ub294 $N$\uac1c\uc758 \uc815\uc218 $B_1, B_2, \\cdots, B_N$\uc744 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ud574 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"31722","problem_lang":"1","title":"Landscape Painting","description":"<p>Yunee&rsquo;s hobby is drawing. One day, inspired by the mountain behind the school, Yunee drew a landscape painting. The landscape painting is a grid with $N$ rows and $M$ columns, where each cell is painted black or white.<\/p>\r\n\r\n<p>Yunee decided to gift the landscape painting to Ponix and Dalgoo. However, there was only one painting, sparking a debate between them about who should take it. The debate wasn&rsquo;t easily finished because Ponix and Dalgoo had different criteria for what they considered a good landscape painting.<\/p>\r\n\r\n<p>Dalgoo thinks a landscape painting with many mountains is good, while Ponix thinks a landscape painting with many lakes is good. The definitions of mountains and lakes are as follows. $(i,j)$ represents the cell at the $i$-th row and $j$-th column.<\/p>\r\n\r\n<ul>\r\n\t<li>If every cell $(a,b)$ satisfying $a\\le x,|a-x|+|b-y|\\le d-1$ is black, then it&rsquo;s called a mountain of size $d$ centered at $(x,y)$. Here, $d$ must be an integer from $1$ to $\\min(y,M-y+1,x)$.<\/li>\r\n\t<li>If every cell $(a,b)$ satisfying $x\\le a\\le x+d-1,y\\le b\\le y+d-1$ is white, then it&rsquo;s called a lake of size $d$ with the top left corner at $(x,y)$. Here, $d$ must be an integer from $1$ to $\\min(N-x+1,M-y+1)$.<\/li>\r\n<\/ul>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/338071b3-59b1-4060-8c7c-7a68e63a61d9\/-\/preview\/\" style=\"height: 225px; width: 300px;\" \/><\/p>\r\n\r\n<p>In the given illustration, there is a mountain centered at $(3,2)$ with a size of $2$ and a lake with the top left corner at $(1,3)$ and a size of $2$.<\/p>\r\n\r\n<p>To stop the debate among friends, Yunee wants to calculate the number of mountains and lakes of each size from $1$ to $N$. Help Yunee solve the problem.<\/p>\r\n","input":"<p>The first line of input contains two space-separated integers $N$ and $M$, denoting the number of rows&nbsp;and&nbsp;the number of columns, respectively. $(1 \\le N, M \\le 2000)$<\/p>\r\n\r\n<p>The following $N$ lines of input contain the landscape painting. Each line contains a string of length $M$, consisting of <span style=\"color:#e74c3c;\"><code>#<\/code><\/span> or <code><span style=\"color:#e74c3c;\">.<\/span><\/code>, where <code><span style=\"color:#e74c3c;\">#<\/span><\/code> represents black and <span style=\"color:#e74c3c;\"><code>.<\/code><\/span> represents white.<\/p>\r\n","output":"<p>On the first line, print $N$ space-separated integers $A_1, A_2, \\cdots, A_N$, representing the number of mountains with size $i$.<\/p>\r\n\r\n<p>On the second line, print $N$ space-separated integers $B_1, B_2, \\cdots, B_N$, representing the number of lakes with size $i$.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English"}]