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문제

동규는 단면 PCB 회로를 설계하려고 한다. PCB 회로는 부품을 장착하는 곳인 패드와, 패드를 잇는 도선으로 구성된다. 회로를 그릴 PCB는 무한한 2차원 평면, 패드는 평면 위의 점, 도선은 평면 위에서 이어진 선분들로 생각할 수 있다.

동규가 설계하려는 회로에는 $2N$개의 패드가 수평 방향으로 나열되어 있다. 왼쪽에서 $i$번째에 위치한 패드의 좌표는 $(i-1, 0)$이다. 패드마다 $1$번부터 $N$번까지의 번호 중 하나가 붙어 있으며, 같은 번호를 가진 패드는 각각 두 개씩 존재한다.

동규는 번호가 같은 패드 쌍들을 서로 만나지 않는 도선들로 이어야 한다. 각 도선은 $x$축 또는 $y$축에 평행한 하나 이상의 선분이 차례로 이어져 있는 모양이고, 자기 자신과 교차하지 않아야 한다. 또한 도선을 구성하는 각 선분은 길이가 양의 정수여야 한다.

패드의 번호가 순서대로 주어졌을 때, 회로를 설계하는 프로그램을 작성하시오.

입력

첫 번째 줄에 $N$이 주어진다. $(1 ≤ N ≤ 1,000)$

두 번째 줄에 패드의 번호를 나타내는 $2N$개의 정수가 순서대로 주어진다. $i$번째 정수는 왼쪽에서 $i$번째에 위치한 패드의 번호이다.

출력

회로 설계가 불가능하다면 NO를 출력한다.

회로 설계가 가능하다면 첫 줄에 YES를 출력한 다음, 회로를 나타내는 $N$개의 줄을 출력한다. $i$번째 줄에는 $i$번 패드 둘을 잇는 도선을 출력한다. 도선의 시작점은 둘 중 왼쪽에 있는 패드, 끝점은 오른쪽에 있는 패드이며, 도선을 출력하는 형식은 다음과 같다.

  • 도선을 구성하는 선분의 개수를 출력한다.
  • 도선을 구성하는 선분을 순서대로 그리는 과정을 다음과 같이 출력한다. 시작점 또는 이전 선분을 그리고 난 뒤의 위치에서 시작해서, 다음 선분을 어느 방향으로 그릴지와 어느 길이만큼 그릴지를 각각 출력한다. 끝점에 도달할 때까지 반복한다. 방향을 나타내는 문자는 U, D, L, R 중 하나이며, 각각 위, 아래, 왼쪽, 오른쪽을 나타낸다.

또한 구성된 회로는 다음 조건을 만족해야 한다. 회로 설계가 가능하다면 아래 조건을 만족하는 회로가 존재함이 보장된다.

  • 각 도선을 구성하는 선분의 개수는 $10$개 이하여야 한다.
  • 도선을 구성하는 선분의 끝점들은 $x, y$ 좌표의 절댓값이 $10,000$ 이하인 정수여야 한다.

가능한 회로가 여러 가지라면 아무거나 하나만 출력한다.

예제 입력 1

4
1 2 3 4 1 2 3 4

예제 출력 1

YES
3 U 1 R 4 D 1
5 D 1 L 2 U 3 R 6 D 2
5 D 2 R 6 U 3 L 2 D 1
3 D 1 R 4 U 1

본문에 주어진 그림과 같이 회로 설계가 가능하다.

예제 입력 2

4
1 2 3 4 1 3 2 4

예제 출력 2

NO

패드를 어떻게 이어도 도선끼리 만나는 일이 생긴다.

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PCB \ud68c\ub85c\ub294 \ubd80\ud488\uc744 \uc7a5\ucc29\ud558\ub294 \uacf3\uc778 \ud328\ub4dc\uc640, \ud328\ub4dc\ub97c \uc787\ub294 \ub3c4\uc120\uc73c\ub85c \uad6c\uc131\ub41c\ub2e4. \ud68c\ub85c\ub97c \uadf8\ub9b4 PCB\ub294 \ubb34\ud55c\ud55c 2\ucc28\uc6d0 \ud3c9\uba74, \ud328\ub4dc\ub294 \ud3c9\uba74 \uc704\uc758 \uc810, \ub3c4\uc120\uc740 \ud3c9\uba74 \uc704\uc5d0\uc11c&nbsp;\uc774\uc5b4\uc9c4 \uc120\ubd84\ub4e4\ub85c&nbsp;\uc0dd\uac01\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ub3d9\uaddc\uac00 \uc124\uacc4\ud558\ub824\ub294 \ud68c\ub85c\uc5d0\ub294 $2N$\uac1c\uc758 \ud328\ub4dc\uac00 \uc218\ud3c9 \ubc29\ud5a5\uc73c\ub85c \ub098\uc5f4\ub418\uc5b4 \uc788\ub2e4. \uc67c\ucabd\uc5d0\uc11c $i$\ubc88\uc9f8\uc5d0 \uc704\uce58\ud55c \ud328\ub4dc\uc758 \uc88c\ud45c\ub294 $(i-1, 0)$\uc774\ub2e4. \ud328\ub4dc\ub9c8\ub2e4 $1$\ubc88\ubd80\ud130 $N$\ubc88\uae4c\uc9c0\uc758 \ubc88\ud638 \uc911 \ud558\ub098\uac00 \ubd99\uc5b4 \uc788\uc73c\uba70, \uac19\uc740 \ubc88\ud638\ub97c \uac00\uc9c4 \ud328\ub4dc\ub294 \uac01\uac01 \ub450 \uac1c\uc529 \uc874\uc7ac\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub3d9\uaddc\ub294 <strong>\ubc88\ud638\uac00 \uac19\uc740 \ud328\ub4dc \uc30d<\/strong>\ub4e4\uc744 <strong>\uc11c\ub85c \ub9cc\ub098\uc9c0 \uc54a\ub294 \ub3c4\uc120<\/strong>\ub4e4\ub85c \uc774\uc5b4\uc57c \ud55c\ub2e4. \uac01 \ub3c4\uc120\uc740 $x$\ucd95 \ub610\ub294 $y$\ucd95\uc5d0 \ud3c9\ud589\ud55c \ud558\ub098 \uc774\uc0c1\uc758 \uc120\ubd84\uc774 \ucc28\ub840\ub85c \uc774\uc5b4\uc838 \uc788\ub294 \ubaa8\uc591\uc774\uace0, \uc790\uae30 \uc790\uc2e0\uacfc \uad50\ucc28\ud558\uc9c0 \uc54a\uc544\uc57c \ud55c\ub2e4. \ub610\ud55c \ub3c4\uc120\uc744 \uad6c\uc131\ud558\ub294 \uac01 \uc120\ubd84\uc740 \uae38\uc774\uac00 \uc591\uc758 \uc815\uc218\uc5ec\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ud328\ub4dc\uc758 \ubc88\ud638\uac00 \uc21c\uc11c\ub300\ub85c \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ud68c\ub85c\ub97c \uc124\uacc4\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/79f3f829-d724-4807-9508-803b4e9db47b\/\" style=\"max-width: 100%; width: 480px;\" \/><\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 $N$\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. $(1 &le; N &le; 1,000)$<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\uc5d0 \ud328\ub4dc\uc758 \ubc88\ud638\ub97c \ub098\ud0c0\ub0b4\ub294 $2N$\uac1c\uc758 \uc815\uc218\uac00 \uc21c\uc11c\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. $i$\ubc88\uc9f8 \uc815\uc218\ub294 \uc67c\ucabd\uc5d0\uc11c $i$\ubc88\uc9f8\uc5d0 \uc704\uce58\ud55c \ud328\ub4dc\uc758 \ubc88\ud638\uc774\ub2e4.<\/p>\r\n","output":"<p>\ud68c\ub85c \uc124\uacc4\uac00 \ubd88\uac00\ub2a5\ud558\ub2e4\uba74 <samp>NO<\/samp>\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ud68c\ub85c \uc124\uacc4\uac00 \uac00\ub2a5\ud558\ub2e4\uba74 \uccab \uc904\uc5d0 <samp>YES<\/samp>\ub97c \ucd9c\ub825\ud55c \ub2e4\uc74c, \ud68c\ub85c\ub97c \ub098\ud0c0\ub0b4\ub294 $N$\uac1c\uc758 \uc904\uc744 \ucd9c\ub825\ud55c\ub2e4. $i$\ubc88\uc9f8 \uc904\uc5d0\ub294 $i$\ubc88 \ud328\ub4dc \ub458\uc744 \uc787\ub294 \ub3c4\uc120\uc744 \ucd9c\ub825\ud55c\ub2e4. \ub3c4\uc120\uc758 \uc2dc\uc791\uc810\uc740 \ub458 \uc911 \uc67c\ucabd\uc5d0 \uc788\ub294 \ud328\ub4dc, \ub05d\uc810\uc740 \uc624\ub978\ucabd\uc5d0 \uc788\ub294 \ud328\ub4dc\uc774\uba70, \ub3c4\uc120\uc744 \ucd9c\ub825\ud558\ub294 \ud615\uc2dd\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\ub3c4\uc120\uc744 \uad6c\uc131\ud558\ub294 \uc120\ubd84\uc758 \uac1c\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/li>\r\n\t<li>\ub3c4\uc120\uc744 \uad6c\uc131\ud558\ub294 \uc120\ubd84\uc744 \uc21c\uc11c\ub300\ub85c \uadf8\ub9ac\ub294 \uacfc\uc815\uc744 \ub2e4\uc74c\uacfc \uac19\uc774 \ucd9c\ub825\ud55c\ub2e4. \uc2dc\uc791\uc810 \ub610\ub294 \uc774\uc804 \uc120\ubd84\uc744 \uadf8\ub9ac\uace0 \ub09c \ub4a4\uc758 \uc704\uce58\uc5d0\uc11c \uc2dc\uc791\ud574\uc11c, \ub2e4\uc74c \uc120\ubd84\uc744 \uc5b4\ub290 \ubc29\ud5a5\uc73c\ub85c \uadf8\ub9b4\uc9c0\uc640 \uc5b4\ub290 \uae38\uc774\ub9cc\ud07c \uadf8\ub9b4\uc9c0\ub97c \uac01\uac01 \ucd9c\ub825\ud55c\ub2e4. \ub05d\uc810\uc5d0 \ub3c4\ub2ec\ud560 \ub54c\uae4c\uc9c0 \ubc18\ubcf5\ud55c\ub2e4. \ubc29\ud5a5\uc744 \ub098\ud0c0\ub0b4\ub294 \ubb38\uc790\ub294 <samp>U,&nbsp;D, L, R<\/samp> \uc911 \ud558\ub098\uc774\uba70, \uac01\uac01 \uc704, \uc544\ub798, \uc67c\ucabd, \uc624\ub978\ucabd\uc744 \ub098\ud0c0\ub0b8\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\ub610\ud55c \uad6c\uc131\ub41c \ud68c\ub85c\ub294 \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\ud574\uc57c \ud55c\ub2e4. \ud68c\ub85c \uc124\uacc4\uac00 \uac00\ub2a5\ud558\ub2e4\uba74 \uc544\ub798 \uc870\uac74\uc744 \ub9cc\uc871\ud558\ub294 \ud68c\ub85c\uac00 \uc874\uc7ac\ud568\uc774 \ubcf4\uc7a5\ub41c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uac01 \ub3c4\uc120\uc744 \uad6c\uc131\ud558\ub294 \uc120\ubd84\uc758 \uac1c\uc218\ub294 $10$\uac1c \uc774\ud558\uc5ec\uc57c \ud55c\ub2e4.<\/li>\r\n\t<li>\ub3c4\uc120\uc744 \uad6c\uc131\ud558\ub294 \uc120\ubd84\uc758 \ub05d\uc810\ub4e4\uc740 $x, y$ \uc88c\ud45c\uc758 \uc808\ub313\uac12\uc774 $10,000$ \uc774\ud558\uc778 \uc815\uc218\uc5ec\uc57c \ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uac00\ub2a5\ud55c \ud68c\ub85c\uac00 \uc5ec\ub7ec \uac00\uc9c0\ub77c\uba74 \uc544\ubb34\uac70\ub098 \ud558\ub098\ub9cc \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","sample_explain_1":"<p>\ubcf8\ubb38\uc5d0 \uc8fc\uc5b4\uc9c4 \uadf8\ub9bc\uacfc \uac19\uc774 \ud68c\ub85c \uc124\uacc4\uac00 \uac00\ub2a5\ud558\ub2e4.<\/p>\r\n","sample_explain_2":"<p>\ud328\ub4dc\ub97c \uc5b4\ub5bb\uac8c \uc774\uc5b4\ub3c4 \ub3c4\uc120\ub07c\ub9ac \ub9cc\ub098\ub294 \uc77c\uc774 \uc0dd\uae34\ub2e4.<\/p>\r\n"},{"problem_id":"20534","problem_lang":"1","title":"Designing a PCB","description":"<p>Dongkyu is trying to design a single-sided printed circuit board (PCB for short). A PCB is composed of pads on which components can be mounted, and conductive tracks connecting the pads. You can think of a PCB as an infinite two-dimensional plane, a pad as a point on the plane, and a track as a connected polyline on the plane.<\/p>\r\n\r\n<p>In the circuit that Dongkyu wants to design, the $2n$ pads are arranged horizontally. The $i$-th pad from the left is located at coordinate $(i - 1, 0)$. Each pad is assigned a label: an integer between $1$ and $n$, inclusive. For each $1 \\le i \\le n$, there are exactly 2 pads labeled with $i$.<\/p>\r\n\r\n<p>Dongkyu needs to draw $n$ tracks to connect the pairs of pads with the same label. Each track must be a polyline consisting of segments of positive integer lengths, such that each segment is parallel to one of the coordinate axes. They start and end at the points representing the pads. No two tracks may share a common point.<\/p>\r\n\r\n<p>Given the number of pads and the labeling, write a program to design the circuit.<\/p>\r\n","input":"<p>The first line of input contains a single integer $n$ ($1 \\le n \\le 1000$).<\/p>\r\n\r\n<p>The second line contains $2 n$ integers $p_i$ ($1 \\le p_i \\le n$). Here, $p_i$ is the label on the $i$-th pad from the left. It is guaranteed that each integer between $1$ and $n$ appears exactly twice in the labels.<\/p>\r\n","output":"<p>If it is impossible to design a circuit conforming to the limitations described in the statement, print &quot;<code>NO<\/code>&quot;.<\/p>\r\n\r\n<p>Otherwise, print &quot;<code>YES<\/code>&quot; on the first line. Then, on the next $n$ lines, output the descriptions of $n$ tracks in order of increasing label number of the pads they are connecting.<\/p>\r\n\r\n<p>Each track must be a polyline starting from the <strong>leftmost<\/strong> of the two connected pads. The description of a track starts with one integer $L_i$ ($1 \\le L_i \\le 10$) describing the number of segments forming the track. Each segment is described by one letter for the direction, followed by a positive integer for the segment length. The directions are: `<code>D<\/code>&#39; --- down (decreasing $y$), `<code>U<\/code>&#39; --- up (increasing $y$), `<code>R<\/code>&#39; --- right (increasing $x$), and `<code>L<\/code>&#39; --- left (decreasing $x$). The segments must be listed from the starting pad to the ending pad in the order they are connected.<\/p>\r\n\r\n<p>Each polyline must have no self-intersections and no self-touchings. Different polylines must have no common points. The resulting coordinates of the vertices of the polylines must be not greater than $10^4$ by absolute value. Separate letters and integers with spaces. Check the sample output to clarify the format.<\/p>\r\n\r\n<p>If there is more than one solution, any one of them will be accepted.<\/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\/690319b7-c33e-459b-8e92-0d515113e82f\/-\/preview\/\" style=\"width: 440px; height: 320px;\" \/><\/p>\r\n\r\n<p>One of the possible circuits for sample 1 is shown at the picture. In sample 2, we cannot connect the pads so that the different tracks do not intersect.<\/p>\r\n"}]