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문제

창영이는 1학년 때 숙제로 했던 이중 연결 리스트 소스를 상근이에게 생일 선물로 보내주었다. 상근이는 드디어 자신이 원하던 기능이 있는 소스를 받게 되어서 매우 기뻤다. 상근이는 하루종일 이 리스트를 가지고 놀려고 한다.

리스트에는 총 N개의 노드가 포함되어 있고, 가장 왼쪽 노드가 1번이며 나머지는 오른쪽으로 갈 수록 1씩 번호가 증가한다. 리스트가 수행할 수 있는 연산은 아래와 같이 2가지이다.

A) 노드 X를 노드 Y의 앞으로 이동

B) 노드 X를 노드 Y의 뒤으로 이동

아래 그림은 노드가 6개인 이중 연결 리스트의 모습이다.

여기에 "A 1 4" 연산을 수행하면 아래와 같이 된다. (노드 1을 노드 4의 앞으로 이동)

그 다음, "B 3 5" 연산을 수행하면 아래 그림과 같은 모습이 된다. (노드 3을 노드 5의 뒤로 이동)

리스트를 가지고 다 논 다음에는 처음 상태로 다시 만들어야 한다. 따라서, 상근이는 리스트에 연산을 입력할 때 마다 종이에 적어두었다.

상근이가 입력한 연산이 모두 주어졌을 때, 처음 상태로 만들기 위해 리스트가 수행해야 하는 연산을 구하는 프로그램을 작성하시오. 이때, 연산을 되도록 적게 사용해야 한다.

입력

첫째 줄에 노드의 수 N과 연산의 수 M이 주어진다. (2 ≤ N ≤ 500,000, 0 ≤ M ≤ 100,000)

다음 M개 줄에는 상근이가 입력한 연산이 문제 설명에 나온 형식으로 주어진다.

출력

첫째 줄에 처음 상태로 만들기 위해서 필요한 연산의 최솟값을 출력한다. 이 값을 K라고 한다.

다음 K개 줄에는 리스트가 수행해야 하는 연산을 순서대로 출력한다.

예제 입력 1

2 1
A 2 1

예제 출력 1

1
A 1 2
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(\ub178\ub4dc 1\uc744 \ub178\ub4dc 4\uc758 \uc55e\uc73c\ub85c \uc774\ub3d9)<\/p>\r\n\r\n<p>\r\n\t<img alt=\"\" src=\"\/upload\/images\/list2.png\" style=\"width: 537px; height: 78px;\" \/><\/p>\r\n\r\n<p>\r\n\t\uadf8 \ub2e4\uc74c, &quot;B 3 5&quot; \uc5f0\uc0b0\uc744 \uc218\ud589\ud558\uba74 \uc544\ub798 \uadf8\ub9bc\uacfc \uac19\uc740 \ubaa8\uc2b5\uc774 \ub41c\ub2e4. (\ub178\ub4dc 3\uc744 \ub178\ub4dc 5\uc758 \ub4a4\ub85c \uc774\ub3d9)<\/p>\r\n\r\n<p>\r\n\t<img alt=\"\" src=\"\/upload\/images\/list3.png\" style=\"width: 537px; height: 78px;\" \/><\/p>\r\n\r\n<p>\r\n\t\ub9ac\uc2a4\ud2b8\ub97c \uac00\uc9c0\uace0 \ub2e4 \ub17c \ub2e4\uc74c\uc5d0\ub294 \ucc98\uc74c \uc0c1\ud0dc\ub85c \ub2e4\uc2dc \ub9cc\ub4e4\uc5b4\uc57c \ud55c\ub2e4. \ub530\ub77c\uc11c, \uc0c1\uadfc\uc774\ub294 \ub9ac\uc2a4\ud2b8\uc5d0 \uc5f0\uc0b0\uc744 \uc785\ub825\ud560 \ub54c \ub9c8\ub2e4 \uc885\uc774\uc5d0 \uc801\uc5b4\ub450\uc5c8\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\uc0c1\uadfc\uc774\uac00 \uc785\ub825\ud55c \uc5f0\uc0b0\uc774 \ubaa8\ub450 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ucc98\uc74c \uc0c1\ud0dc\ub85c \ub9cc\ub4e4\uae30 \uc704\ud574 \ub9ac\uc2a4\ud2b8\uac00 \uc218\ud589\ud574\uc57c \ud558\ub294 \uc5f0\uc0b0\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624. \uc774\ub54c, \uc5f0\uc0b0\uc744 \ub418\ub3c4\ub85d \uc801\uac8c \uc0ac\uc6a9\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n","input":"\r\n<p>\r\n\t\uccab\uc9f8 \uc904\uc5d0 \ub178\ub4dc\uc758 \uc218 N\uacfc \uc5f0\uc0b0\uc758 \uc218 M\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (2 &le; N &le; 500,000, 0 &le; M &le; 100,000)<\/p>\r\n\r\n<p>\r\n\t\ub2e4\uc74c M\uac1c \uc904\uc5d0\ub294 \uc0c1\uadfc\uc774\uac00 \uc785\ub825\ud55c \uc5f0\uc0b0\uc774 \ubb38\uc81c \uc124\uba85\uc5d0 \ub098\uc628 \ud615\uc2dd\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\r\n\t\uccab\uc9f8 \uc904\uc5d0 \ucc98\uc74c \uc0c1\ud0dc\ub85c \ub9cc\ub4e4\uae30 \uc704\ud574\uc11c \ud544\uc694\ud55c \uc5f0\uc0b0\uc758 \ucd5c\uc19f\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4. \uc774 \uac12\uc744 K\ub77c\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\ub2e4\uc74c K\uac1c \uc904\uc5d0\ub294 \ub9ac\uc2a4\ud2b8\uac00 \uc218\ud589\ud574\uc57c \ud558\ub294 \uc5f0\uc0b0\uc744 \uc21c\uc11c\ub300\ub85c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"3045","problem_lang":"1","title":"LISTA","description":"<p>Mirko received a birthday present from his aunt in the US &ndash; a brand-new doubly-linked list (an example of which is shown in the figure below). The list contains N nodes numbered 1 through N. Two types of moves can be done on the list:&nbsp;<\/p>\r\n\r\n<p>A) Move node X in front of node Y.&nbsp;<br \/>\r\nB) Move node X after node Y.&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/list1.png\" style=\"height:78px; width:537px\" \/><\/p>\r\n\r\n<p>An example of a list with 6 nodes.&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/list2.png\" style=\"height:78px; width:537px\" \/><\/p>\r\n\r\n<p>The list after the move &quot;A 1 4&quot;.&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/list3.png\" style=\"height:78px; width:537px\" \/><\/p>\r\n\r\n<p>The list after another move, &quot;B 3 5&quot;.&nbsp;<\/p>\r\n\r\n<p>Mirko played with his new toy for hours, writing down each move on a piece of paper so that he can reconstruct the list&#39;s initial state (nodes 1 through N in order from left to right).&nbsp;<\/p>\r\n\r\n<p>When he decided to reconstruct the list, Mirko was astonished to find that there is no easy way to invert the moves and restore the list&#39;s initial state. Mirko cannot know where node X was prior to each move, only where it ended up.&nbsp;<\/p>\r\n\r\n<p>Seeing how Mirko is still recovering from the shock, write a program that finds a minimal sequence of moves that restored the list&#39;s initial state from Mirko&#39;s logs.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","input":"<p>The first line of input contains two integers N and K (2 &le; N &le; 500 000, 0 &le; M &le; 100 000), the number of nodes and the number of moves made by Mirko.&nbsp;<\/p>\r\n\r\n<p>Each of the next M rows contains a description of a single move made by Mirko &ndash; the type of move (&#39;A&#39; or &#39;B&#39;) and two integers X and Y.&nbsp;<\/p>\r\n","output":"<p>Output the minimum number of moves (call this number K) on the first line.&nbsp;<\/p>\r\n\r\n<p>Each of the next K lines should contain a description of a single move in the same format as in the input.&nbsp;<\/p>\r\n\r\n<p>Note: The sequence need not be unique.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]