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문제

큐 Q, 스택 A, 스택 B와 다음과 같은 연산이 있다.

QA(n): Q에서 수 하나를 빼고, A에 넣는다. 이 작업을 n번 반복한다.

QB(n): Q에서 수 하나를 빼고, B에 넣는다. 이 작업을 n번 반복한다.

QQ(n): Q에서 수 하나를 빼고, Q에 넣는다. 이 작업을 n번 반복한다.

AQ(n): A에서 수 하나를 빼고, Q에 넣는다. 이 작업을 n번 반복한다.

BQ(n): B에서 수 하나를 빼고, Q에 넣는다. 이 작업을 n번 반복한다.

AB(n): A에서 수 하나를 빼고, B에 넣는다. 이 작업을 n번 반복한다.

BA(n): B에서 수 하나를 빼고, A에 넣는다. 이 작업을 n번 반복한다.

위의 연산은 n의 값에 상관없이 모두 각각 한 번으로 친다.

처음에 큐에 수가 이미 채워져 있고, 두 스택은 비어있다. 이 때, 큐에 수를 오름차순으로 만들때 필요한 연산의 최소값은 몇 번일까?

예를 들어, 큐에 수가 (4 3 1 2 0)과 같이 채워져 있다고 하자. 이 때, 큐는 다음과 같이 3번만에 정렬할 수 있다. QA(2), QQ(2), AQ(2) 

또, (5 4 1 3 2 0)과 같이 채워져 있다면, 4번만에 정렬할 수 있다. QB(2), QQ(1), QB(2), BQ(4)

큐에 들어있는 수를 정렬하기 위해 필요한 연산의 최소값을 구하는 프로그램을 작성하시오.

입력

입력은 여러 테스트 케이스로 이루어져 있다. 각 테스트 케이스는 한 줄로 이루어져 있다. 첫번째 숫자는 큐에 들어있는 수의 개수 N이다. 다음 N개의 수는 큐에 들어있는 수가 앞에서부터 순서대로 주어진다. 큐에 들어있는 수는 모두 0보다 크거나 같고, N-1보다 작거나 같은 정수이다. 또, 한 숫자는 한 번씩만 주어진다. N은 10을 넘지 않는다.

입력의 마지막 줄에는 0이 하나 주어진다.

출력

각 테스트 케이스에 대해서, 큐를 정렬하는데 필요한 연산의 최소값을 출력한다.

예제 입력 1

5 4 3 1 2 0
6 5 4 1 3 2 0
0

예제 출력 1

3
4

힌트

[{"problem_id":"4931","problem_lang":"0","title":"\ud050 \uc18c\ud2b8","description":"<p>\r\n\t\ud050 Q, \uc2a4\ud0dd A, \uc2a4\ud0dd B\uc640 \ub2e4\uc74c\uacfc \uac19\uc740 \uc5f0\uc0b0\uc774 \uc788\ub2e4.<\/p>\r\n\r\n<p>\r\n\t<strong>QA(n)<\/strong>: Q\uc5d0\uc11c \uc218 \ud558\ub098\ub97c \ube7c\uace0, A\uc5d0 \ub123\ub294\ub2e4. \uc774 \uc791\uc5c5\uc744 n\ubc88 \ubc18\ubcf5\ud55c\ub2e4.<\/p>\r\n<p>\r\n\t<strong>QB(n)<\/strong>: Q\uc5d0\uc11c \uc218 \ud558\ub098\ub97c \ube7c\uace0, B\uc5d0 \ub123\ub294\ub2e4. \uc774 \uc791\uc5c5\uc744 n\ubc88 \ubc18\ubcf5\ud55c\ub2e4.<\/p>\r\n<p>\r\n\t<strong>QQ(n)<\/strong>: Q\uc5d0\uc11c \uc218 \ud558\ub098\ub97c \ube7c\uace0, Q\uc5d0 \ub123\ub294\ub2e4. \uc774 \uc791\uc5c5\uc744 n\ubc88 \ubc18\ubcf5\ud55c\ub2e4.<\/p>\r\n<p>\r\n\t<strong>AQ(n)<\/strong>: A\uc5d0\uc11c \uc218 \ud558\ub098\ub97c \ube7c\uace0, Q\uc5d0 \ub123\ub294\ub2e4. \uc774 \uc791\uc5c5\uc744 n\ubc88 \ubc18\ubcf5\ud55c\ub2e4.<\/p>\r\n<p>\r\n\t<strong>BQ(n)<\/strong>: B\uc5d0\uc11c \uc218 \ud558\ub098\ub97c \ube7c\uace0, Q\uc5d0 \ub123\ub294\ub2e4. \uc774 \uc791\uc5c5\uc744 n\ubc88 \ubc18\ubcf5\ud55c\ub2e4.<\/p>\r\n<p>\r\n\t<strong>AB(n)<\/strong>: A\uc5d0\uc11c \uc218 \ud558\ub098\ub97c \ube7c\uace0, B\uc5d0 \ub123\ub294\ub2e4. \uc774 \uc791\uc5c5\uc744 n\ubc88 \ubc18\ubcf5\ud55c\ub2e4.<\/p>\r\n<p>\r\n\t<strong>BA(n)<\/strong>: B\uc5d0\uc11c \uc218 \ud558\ub098\ub97c \ube7c\uace0, A\uc5d0 \ub123\ub294\ub2e4. \uc774 \uc791\uc5c5\uc744 n\ubc88 \ubc18\ubcf5\ud55c\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\uc704\uc758 \uc5f0\uc0b0\uc740 n\uc758 \uac12\uc5d0 \uc0c1\uad00\uc5c6\uc774 \ubaa8\ub450 \uac01\uac01 \ud55c \ubc88\uc73c\ub85c \uce5c\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\ucc98\uc74c\uc5d0 \ud050\uc5d0 \uc218\uac00 \uc774\ubbf8 \ucc44\uc6cc\uc838 \uc788\uace0, \ub450 \uc2a4\ud0dd\uc740 \ube44\uc5b4\uc788\ub2e4. \uc774 \ub54c, \ud050\uc5d0 \uc218\ub97c \uc624\ub984\ucc28\uc21c\uc73c\ub85c \ub9cc\ub4e4\ub54c \ud544\uc694\ud55c \uc5f0\uc0b0\uc758 \ucd5c\uc18c\uac12\uc740 \uba87 \ubc88\uc77c\uae4c?<\/p>\r\n\r\n<p>\r\n\t\uc608\ub97c \ub4e4\uc5b4, \ud050\uc5d0 \uc218\uac00 (4 3 1 2 0)\uacfc \uac19\uc774 \ucc44\uc6cc\uc838 \uc788\ub2e4\uace0 \ud558\uc790. \uc774 \ub54c, \ud050\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 3\ubc88\ub9cc\uc5d0 \uc815\ub82c\ud560 \uc218 \uc788\ub2e4. QA(2), QQ(2), AQ(2)&nbsp;<\/p>\r\n<p>\r\n\t\ub610, (5 4 1 3 2 0)\uacfc \uac19\uc774 \ucc44\uc6cc\uc838 \uc788\ub2e4\uba74, 4\ubc88\ub9cc\uc5d0 \uc815\ub82c\ud560 \uc218 \uc788\ub2e4. QB(2), QQ(1), QB(2), BQ(4)<\/p>\r\n\r\n<p>\r\n\t\ud050\uc5d0 \ub4e4\uc5b4\uc788\ub294 \uc218\ub97c \uc815\ub82c\ud558\uae30 \uc704\ud574 \ud544\uc694\ud55c \uc5f0\uc0b0\uc758 \ucd5c\uc18c\uac12\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"\r\n<p>\r\n\t\uc785\ub825\uc740 \uc5ec\ub7ec \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ud55c \uc904\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uccab\ubc88\uc9f8 \uc22b\uc790\ub294 \ud050\uc5d0 \ub4e4\uc5b4\uc788\ub294 \uc218\uc758 \uac1c\uc218 N\uc774\ub2e4. \ub2e4\uc74c N\uac1c\uc758 \uc218\ub294 \ud050\uc5d0 \ub4e4\uc5b4\uc788\ub294 \uc218\uac00 \uc55e\uc5d0\uc11c\ubd80\ud130 \uc21c\uc11c\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \ud050\uc5d0 \ub4e4\uc5b4\uc788\ub294 \uc218\ub294 \ubaa8\ub450 0\ubcf4\ub2e4 \ud06c\uac70\ub098 \uac19\uace0, N-1\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\uc740 \uc815\uc218\uc774\ub2e4. \ub610, \ud55c \uc22b\uc790\ub294 \ud55c \ubc88\uc529\ub9cc \uc8fc\uc5b4\uc9c4\ub2e4. N\uc740 10\uc744 \ub118\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\uc785\ub825\uc758 \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 0\uc774 \ud558\ub098 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\r\n\t\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c, \ud050\ub97c \uc815\ub82c\ud558\ub294\ub370 \ud544\uc694\ud55c \uc5f0\uc0b0\uc758 \ucd5c\uc18c\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"4931","problem_lang":"1","title":"Sort that Queue","description":"<p>Given a queue Q, a stack A, and a stack B, and the following operations:<\/p>\r\n\r\n<p><strong>QA(n)<\/strong>: dequeue an item from Q, pushing it on A; repeat n times<br \/>\r\n<strong>QB(n)<\/strong>: dequeue an item from Q, pushing it on B; repeat n times<br \/>\r\n<strong>QQ(n)<\/strong>: dequeue an item from Q, enqueue it again in Q; repeat n times<br \/>\r\n<strong>AQ(n)<\/strong>: pop an item from A, enqueue it in Q; repeat n times<br \/>\r\n<strong>BQ(n)<\/strong>: pop an item from B, enqueue it in Q; repeat n times<br \/>\r\n<strong>AB(n)<\/strong>: pop an item from A, push it on B; repeat n times<br \/>\r\n<strong>BA(n)<\/strong>: pop an item from B, push it on A; repeat n times.<\/p>\r\n\r\n<p>Note that each of the above is considered a single operation, regardless of the value of n.<\/p>\r\n\r\n<p>Now assume that the queue is already populated with numbers and that both stacks are empty, what is the minimum number of operations needed to have the same numbers in the queue but sorted in an ascending order? (smallest in front.)<\/p>\r\n\r\n<p>For example, the queue (4 3 1 2 0) where 4 is at the front, can be sorted in three steps as follows: QA(2), QQ(2), then AQ(2). The queue (5 4 1 3 2 0) can be sorted in four operations as follows: QB(2), QQ(1), QB(2), BQ(4).<\/p>\r\n\r\n<p>Write a program that determines the minimum number of operations needed to sort a given queue.<\/p>\r\n","input":"<p>Your program will be tested on a number of test cases. Each test case is speci\ufb01ed on a single line. Each test case is made of N + 1 integers. The \ufb01rst integer speci\ufb01es N which is the number of elements in the queue. A queue of N elements will have in it the integers from 0 to N &minus; 1 in some random order. The integers in the queue are speci\ufb01ed from the front of the queue to the back. No queue will have more than 10 elements.<\/p>\r\n\r\n<p>The end of the test cases is identi\ufb01ed with an input line that contains a single integer N = 0 (which is not part of the test cases.)<\/p>\r\n","output":"<p>For each test case, write the result on a separate line.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]