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문제

지민이는 지뢰 사건에 의해 정문이에게 도망 다니고 있다. 그러던 중 N개의 펜스로 설치된 장애물을 만나게 되었다. 이 펜스들은 x축과 평행하고 i번째 펜스의 y좌표는 i이다. 펜스는 너무 높기 때문에 넘을 수 없고 돌아가는 방법만이 가능하다. 또한 현재 위치에서 x축의 양의 방향 또는 음의 방향으로 진행하던 중 펜스의 끝에 도달하면 y축과 평행하게 다음 펜스를 만날 때까지 내려가는 일을 반복한다.

   +-+-S-+             4번째 펜스
 +-+-+-+               3번째 펜스
     +-+-+-+           2번째 펜스
   +-+-+-+             1번째 펜스
 |=|=|=*=|=|=|         
-3-2-1 0 1 2 3 

위의 그림에서 S는 현재 지민이가 있는 위치이다. 그리고 지민이는 펜스를 잘 피하여 *로 표시된 탈출구까지 도달해야한다. 가능한 경로 중 하나는 일단 현재 위치에서 x축과 평행하게 양의 방향으로 1만큼 이동하면 펜스의 끝에 도달한다. 그리고 y축과 평행하게 아래로 내려가면 2번째 펜스에 도달하게 되고 또 다시 1만큼 x좌표가 양인 방향으로 이동하면 펜스의 끝에 도달하게 된다. 그리고 1만큼 내려간 뒤 x좌표가 음인 방향으로 2만큼 이동하면 탈출구에 도달하여 탈출할 수 있다.  y축을 따라 내려가는 길이는 어떤 식으로 내려가든 일정하기 때문에 고려하지 않는다고 하면 위의  경로로 이동한 것은 x축과 평행하게 총 4만큼 이동한 게 된다. 그리고 위의 경로가 이 예에서 최단 경로이다. 문제는 펜스의 위치가 주어졌을 때 최단경로의 길이를 구하는 것이다.

입력

첫째 줄에 펜스의 개수 N(1 ≤ N ≤ 50,000)과 지민이가 있는 x좌표 S(-100,000 ≤ S ≤ 100,000)가 공백으로 구분되어 주어진다.

두 번째 줄부터 N+1번째 줄까지 펜스의 시작 좌표 x와 끝 좌표 x가 공백으로 구분되어 주어진다. 좌표의 범위는 -100,000 이상 100,000 이하이다.

출력

탈출구로 도달하는 최단경로를 출력한다.

예제 입력 1

4 0
-2 1
-3 0
-1 2
-2 1

예제 출력 1

4
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The course consists of a sequence of N fences (1 &lt;= N &lt;= 50,000) of varying lengths, each parallel to the x axis. Fence i&#39;s y coordinate is i.&nbsp;<\/p>\r\n\r\n<p>The door to FJ&#39;s barn is at the origin (marked &#39;*&#39; below). The starting point of the course lies at coordinate (S,N).&nbsp;<\/p>\r\n\r\n<pre>\r\n   +-S-+-+-+        (fence #N)\r\n +-+-+-+            (fence #N-1)\r\n     ...               ...\r\n   +-+-+-+          (fence #2)\r\n     +-+-+-+        (fence #1)\r\n=|=|=|=*=|=|=|      (barn)\r\n-3-2-1 0 1 2 3    \r\n<\/pre>\r\n\r\n<p>FJ&#39;s original intention was for the cows to jump over the fences, but cows are much more comfortable keeping all four hooves on the ground. Thus, they will walk along the fence and, when the fence ends, they will turn towards the x axis and continue walking in a straight line until they hit another fence segment or the side of the barn. Then they decide to go left or right until they reach the end of the fence segment, and so on, until they finally reach the side of the barn and then, potentially after a short walk, the ending point.&nbsp;<\/p>\r\n\r\n<p>Naturally, the cows want to walk as little as possible. Find the minimum distance the cows have to travel back and forth to get from the starting point to the door of the barn.<\/p>\r\n","input":"<p>* Line 1: Two space-separated integers: N and S (-100,000 &lt;= S &lt;= 100,000)&nbsp;<\/p>\r\n\r\n<p>* Lines 2..N+1: Each line contains two space-separated integers: A_i and B_i (-100,000 &lt;= A_i &lt; B_i &lt;= 100,000), the starting and ending x-coordinates of fence segment i. Line 2 describes fence #1; line 3 describes fence #2; and so on. The starting position will satisfy A_N &lt;= S &lt;= B_N. Note that the fences will be traversed in reverse order of the input sequence.<\/p>\r\n","output":"<p>* Line 1: The minimum distance back and forth in the x direction required to get from the starting point to the ending point by walking around the fences. The distance in the y direction is not counted, since it is always precisely N.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_code":"\uc601\uc5b4"}]

출처

Olympiad > USA Computing Olympiad > 2004-2005 Season > USACO December 2004 Contest > Gold 2번

  • 문제의 오타를 찾은 사람: Acka
  • 문제를 번역한 사람: author6
  • 잘못된 조건을 찾은 사람: ntopia