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문제

소가 왜 길을 건너는지는 미해결 난제지만, 농부 존의 소들이 길을 자주 건넌다는 것은 잘 알려진 사실이다. 소들이 길을 건너는 일이 너무 잦아서 건너면서 부딪히는 일도 생기는데, 존은 이 상황을 해결하고 싶다.

농장에는 일자형 길이 있고, 양쪽에 목초지가 N개씩 (1 ≤ N ≤ 100,000) 있다. 종별로 목초지 구조가 너무 달라서 한 목초지에는 정해진 종의 소만 방목할 수 있다. i번 목초지에는 i번 소만 방목할 수 있는 것이다. 소가 길을 건널 때는 자신의 종을 방목하는 반대편의 목초지로 이동하는 것이다.

목초지의 순서가 뒤죽박죽이어서, a종의 소와 b종의 소가 건너는 길이 겹칠 수도 있다. 존이 목초지 건설에 주의를 기울이지 않은 탓이다. 이 때 (a,b)를 "가로지르는 쌍"이라고 하자.

존은 가로지르는 쌍의 수를 최소화하기 위해 농장을 옮기는 방법을 고안했다. 0 ≤ k < N인 정수 k에 대해, 맨 뒤에 있는 목초지 k개를 맨 앞으로 옮길 것이다. 예를 들어서, 목초지 번호가 차례대로 3, 7, 1, 2, 5, 4, 6이고 k=2라면, 옮긴 후의 목초지 번호는 4, 6, 3, 7, 1, 2, 5가 된다. 길의 왼쪽에 있는 목초지여도 되고 오른쪽이어도 되지만, 둘 중 하나만 된다. 가로지르는 쌍을 최소로 할 수 있도록 존을 도와주자.

입력

첫 줄에 N이 주어진다. 다음 N줄에는 길의 왼쪽에 있는 목초지 번호가 차례대로 주어진다. 각 종은 한 번씩 나타난다. 그 다음 N줄에는 길의 오른쪽에 있는 목초지가 같은 방식으로 주어진다.

출력

가로지르는 쌍의 최소 개수를 출력한다.

예제 입력 1

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예제 출력 1

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[{"problem_id":"14458","problem_lang":"0","title":"\uc18c\uac00 \uae38\uc744 \uac74\ub108\uac04 \uc774\uc720 10","description":"<p>\uc18c\uac00 \uc65c \uae38\uc744 \uac74\ub108\ub294\uc9c0\ub294 \ubbf8\ud574\uacb0 \ub09c\uc81c\uc9c0\ub9cc, \ub18d\ubd80 \uc874\uc758 \uc18c\ub4e4\uc774 \uae38\uc744 \uc790\uc8fc \uac74\ub10c\ub2e4\ub294 \uac83\uc740 \uc798 \uc54c\ub824\uc9c4 \uc0ac\uc2e4\uc774\ub2e4. \uc18c\ub4e4\uc774 \uae38\uc744 \uac74\ub108\ub294 \uc77c\uc774 \ub108\ubb34 \uc7a6\uc544\uc11c \uac74\ub108\uba74\uc11c \ubd80\ub52a\ud788\ub294 \uc77c\ub3c4 \uc0dd\uae30\ub294\ub370, \uc874\uc740 \uc774 \uc0c1\ud669\uc744 \ud574\uacb0\ud558\uace0 \uc2f6\ub2e4.<\/p>\r\n\r\n<p>\ub18d\uc7a5\uc5d0\ub294 \uc77c\uc790\ud615 \uae38\uc774 \uc788\uace0, \uc591\ucabd\uc5d0 \ubaa9\ucd08\uc9c0\uac00 N\uac1c\uc529 (1 &le; N &le; 100,000) \uc788\ub2e4. \uc885\ubcc4\ub85c \ubaa9\ucd08\uc9c0 \uad6c\uc870\uac00 \ub108\ubb34 \ub2ec\ub77c\uc11c \ud55c \ubaa9\ucd08\uc9c0\uc5d0\ub294 \uc815\ud574\uc9c4 \uc885\uc758 \uc18c\ub9cc \ubc29\ubaa9\ud560 \uc218 \uc788\ub2e4. i\ubc88 \ubaa9\ucd08\uc9c0\uc5d0\ub294 i\ubc88 \uc18c\ub9cc \ubc29\ubaa9\ud560 \uc218 \uc788\ub294 \uac83\uc774\ub2e4. \uc18c\uac00 \uae38\uc744 \uac74\ub110 \ub54c\ub294 \uc790\uc2e0\uc758 \uc885\uc744 \ubc29\ubaa9\ud558\ub294 \ubc18\ub300\ud3b8\uc758 \ubaa9\ucd08\uc9c0\ub85c \uc774\ub3d9\ud558\ub294 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\ubaa9\ucd08\uc9c0\uc758 \uc21c\uc11c\uac00 \ub4a4\uc8fd\ubc15\uc8fd\uc774\uc5b4\uc11c, a\uc885\uc758 \uc18c\uc640 b\uc885\uc758 \uc18c\uac00 \uac74\ub108\ub294 \uae38\uc774 \uacb9\uce60 \uc218\ub3c4 \uc788\ub2e4. \uc874\uc774 \ubaa9\ucd08\uc9c0 \uac74\uc124\uc5d0 \uc8fc\uc758\ub97c \uae30\uc6b8\uc774\uc9c0 \uc54a\uc740 \ud0d3\uc774\ub2e4. \uc774 \ub54c (a,b)\ub97c &quot;\uac00\ub85c\uc9c0\ub974\ub294 \uc30d&quot;\uc774\ub77c\uace0 \ud558\uc790.<\/p>\r\n\r\n<p>\uc874\uc740 \uac00\ub85c\uc9c0\ub974\ub294 \uc30d\uc758 \uc218\ub97c \ucd5c\uc18c\ud654\ud558\uae30 \uc704\ud574 \ub18d\uc7a5\uc744 \uc62e\uae30\ub294 \ubc29\ubc95\uc744 \uace0\uc548\ud588\ub2e4. 0 &le; k &lt; N\uc778 \uc815\uc218 k\uc5d0 \ub300\ud574, \ub9e8 \ub4a4\uc5d0 \uc788\ub294 \ubaa9\ucd08\uc9c0 k\uac1c\ub97c \ub9e8 \uc55e\uc73c\ub85c \uc62e\uae38 \uac83\uc774\ub2e4. \uc608\ub97c \ub4e4\uc5b4\uc11c, \ubaa9\ucd08\uc9c0 \ubc88\ud638\uac00 \ucc28\ub840\ub300\ub85c 3, 7, 1, 2, 5, 4, 6\uc774\uace0 k=2\ub77c\uba74, \uc62e\uae34 \ud6c4\uc758 \ubaa9\ucd08\uc9c0 \ubc88\ud638\ub294 4, 6, 3, 7, 1, 2, 5\uac00 \ub41c\ub2e4. \uae38\uc758 \uc67c\ucabd\uc5d0 \uc788\ub294 \ubaa9\ucd08\uc9c0\uc5ec\ub3c4 \ub418\uace0 \uc624\ub978\ucabd\uc774\uc5b4\ub3c4 \ub418\uc9c0\ub9cc, \ub458 \uc911 \ud558\ub098\ub9cc \ub41c\ub2e4. \uac00\ub85c\uc9c0\ub974\ub294 \uc30d\uc744 \ucd5c\uc18c\ub85c \ud560 \uc218 \uc788\ub3c4\ub85d \uc874\uc744 \ub3c4\uc640\uc8fc\uc790.<\/p>\r\n","input":"<p>\uccab \uc904\uc5d0 N\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ub2e4\uc74c N\uc904\uc5d0\ub294 \uae38\uc758 \uc67c\ucabd\uc5d0 \uc788\ub294 \ubaa9\ucd08\uc9c0 \ubc88\ud638\uac00 \ucc28\ub840\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \uc885\uc740 \ud55c \ubc88\uc529 \ub098\ud0c0\ub09c\ub2e4. \uadf8 \ub2e4\uc74c N\uc904\uc5d0\ub294 \uae38\uc758 \uc624\ub978\ucabd\uc5d0 \uc788\ub294 \ubaa9\ucd08\uc9c0\uac00 \uac19\uc740 \ubc29\uc2dd\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac00\ub85c\uc9c0\ub974\ub294 \uc30d\uc758 \ucd5c\uc18c \uac1c\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"14458","problem_lang":"1","title":"Why Did the Cow Cross the Road (Platinum)","description":"<p>Why did the cow cross the road? We may never know the full reason, but it is certain that Farmer John&#39;s cows do end up crossing the road quite frequently. In fact, they end up crossing the road so often that they often bump into each-other when their paths cross, a situation Farmer John would like to remedy.<\/p>\r\n\r\n<p>Farmer John raises&nbsp;N&nbsp;breeds of cows (1 &le; N &le; 100,000), and each of his fields is dedicated to grazing for one specific breed; for example, a field dedicated to breed 12 can only be used for cows of breed 12 and not of any other breed. A long road runs through his farm. There is a sequence of&nbsp;N&nbsp;fields on one side of the road (one for each breed), and a sequence of&nbsp;N&nbsp;fields on the other side of the road (also one for each breed). When a cow crosses the road, she therefore crosses between the two fields designated for her specific breed.<\/p>\r\n\r\n<p>Had Farmer John planned more carefully, he would have ordered the fields by breed the same way on both sides of the road, so the two fields for each breed would be directly across the road from each-other. This would have allowed cows to cross the road without any cows from different breeds bumping into one-another. Alas, the orderings on both sides of the road might be different, so Farmer John observes that there might be pairs of breeds that cross. A pair of different breeds&nbsp;(a,b) is &quot;crossing&quot; if any path across the road for breed&nbsp;a&nbsp;must intersect any path across the road for breed&nbsp;b.<\/p>\r\n\r\n<p>Farmer John would like to minimize the number of crossing pairs of breeds. For logistical reasons, he figures he can move cows around on one side of the road so the fields on that side undergo a &quot;cyclic shift&quot;. That is, for some&nbsp;0 &le; k &lt; N, every cow re-locates to the field&nbsp;k&nbsp;fields ahead of it, with the cows in the last&nbsp;k&nbsp;fields moving so they now populate the first&nbsp;k&nbsp;fields. For example, if the fields on one side of the road start out ordered by breed as 3, 7, 1, 2, 5, 4, 6 and undergo a cyclic shift by&nbsp;k=2, the new order will be 4, 6, 3, 7, 1, 2, 5. Please determine the minimum possible number of crossing pairs of breeds that can exist after an appropriate cyclic shift of the fields on one side of the road.<\/p>\r\n","input":"<p>The first line of input contains&nbsp;N. The next&nbsp;N&nbsp;lines describe the order, by breed ID, of fields on one side of the road; each breed ID is an integer in the range&nbsp;1&hellip;N. The last N&nbsp;lines describe the order, by breed ID, of the fields on the other side of the road.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","output":"<p>Please output the minimum number of crossing pairs of breeds after a cyclic shift of the fields on one side of the road (either side can be shifted).<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]