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문제

상근이는 점점 부자가 되었고 트럭 운송 회사를 차렸다. 이 회사에는 트럭이 총 N대 있고, 모든 배달은 "공부 고속도로"를 통해 이루어진다.

공부 고속도로에는 나들목(인터체인지, IC)이 1,000,000개 있다. 그리고, 각 나들목은 1번부터 순서대로 번호가 매겨져 있다. 나들목에서는 고속도로로 들어오거나 나갈 수 있다.

고속도로에 들어갈 때는 들어온 나들목의 번호가 적혀있는 티켓을 하나 받게 된다. 이 티켓은 고속도로에서 나갈 때 요금소(톨게이트)에 제시해야하고, 들어온 나들목과 나가는 나들목 번호의 차이만큼 요금을 내야 한다. 예를 들어, 티켓에 적혀있는 나들목의 번호가 30이고 12번 나들목으로 나간다면, 요금은 18원이 된다.

고속도로 이용 요금은 점점 회사가 감당할 수 없는 수준까지 치솟았고, 상근이는 획기적인 방법을 생각해냈다. 바로, 고속도로 중간에서 두 운전사가 만나서 티켓을 교환하는 것이다. 이 방법은 서로 경로가 겹치지 않더라도 교환할 수 있으며, 티켓은 여러 번 교환할 수 있다.

하지만, 의심을 피하기 위해서 티켓에 적혀있는 나들목의 번호와 같은 나들목으로 나갈 수는 없다. 

운전사끼리 티켓을 적절히 교환했을 때, 내야하는 고속도로 이용 요금의 최소값을 구하는 프로그램을 작성하시오.

입력

첫째 줄에 트럭의 수 N이 주어진다. (1 ≤ N ≤ 100,000)

다음 N개 줄에는 각 트럭이 들어온 나들목의 번호와 나가야 하는 나들목의 번호가 공백으로 구분되서 주어진다. 나들목의 번호는 1보다 크거나 같고, 1,000,000보다 작거나 같은 자연수이다.

두 트럭이 고속도로로 들어올 때 사용하는 나들목의 번호나 나갈 때 사용하는 나들목의 번호가 같은 경우는 없다.

출력

상근이네 트럭 운송 회사가 내야하는 고속도로 이용 요금의 최소값을 출력한다. 이 값은 32비트 정수 범위를 넘어갈 수 있기 때문에, 64비트 정수(C/C++: long long)을 사용해야 한다.

예제 입력 1

3
3 65
45 10
60 25

예제 출력 1

32

힌트

[{"problem_id":"2984","problem_lang":"0","title":"\uace0\uc18d\ub3c4\ub85c","description":"<p>\r\n\t\uc0c1\uadfc\uc774\ub294 \uc810\uc810 \ubd80\uc790\uac00 \ub418\uc5c8\uace0 \ud2b8\ub7ed \uc6b4\uc1a1 \ud68c\uc0ac\ub97c \ucc28\ub838\ub2e4. \uc774 \ud68c\uc0ac\uc5d0\ub294 \ud2b8\ub7ed\uc774 \ucd1d N\ub300 \uc788\uace0, \ubaa8\ub4e0 \ubc30\ub2ec\uc740 &quot;\uacf5\ubd80 \uace0\uc18d\ub3c4\ub85c&quot;\ub97c \ud1b5\ud574 \uc774\ub8e8\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\uacf5\ubd80 \uace0\uc18d\ub3c4\ub85c\uc5d0\ub294 \ub098\ub4e4\ubaa9(\uc778\ud130\uccb4\uc778\uc9c0, IC)\uc774 1,000,000\uac1c \uc788\ub2e4. \uadf8\ub9ac\uace0, \uac01 \ub098\ub4e4\ubaa9\uc740 1\ubc88\ubd80\ud130 \uc21c\uc11c\ub300\ub85c \ubc88\ud638\uac00 \ub9e4\uaca8\uc838 \uc788\ub2e4. \ub098\ub4e4\ubaa9\uc5d0\uc11c\ub294 \uace0\uc18d\ub3c4\ub85c\ub85c \ub4e4\uc5b4\uc624\uac70\ub098 \ub098\uac08 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\uace0\uc18d\ub3c4\ub85c\uc5d0 \ub4e4\uc5b4\uac08 \ub54c\ub294 \ub4e4\uc5b4\uc628 \ub098\ub4e4\ubaa9\uc758 \ubc88\ud638\uac00 \uc801\ud600\uc788\ub294 \ud2f0\ucf13\uc744 \ud558\ub098 \ubc1b\uac8c \ub41c\ub2e4. \uc774 \ud2f0\ucf13\uc740 \uace0\uc18d\ub3c4\ub85c\uc5d0\uc11c \ub098\uac08 \ub54c \uc694\uae08\uc18c(\ud1a8\uac8c\uc774\ud2b8)\uc5d0 \uc81c\uc2dc\ud574\uc57c\ud558\uace0, \ub4e4\uc5b4\uc628 \ub098\ub4e4\ubaa9\uacfc \ub098\uac00\ub294 \ub098\ub4e4\ubaa9 \ubc88\ud638\uc758 \ucc28\uc774\ub9cc\ud07c \uc694\uae08\uc744 \ub0b4\uc57c \ud55c\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \ud2f0\ucf13\uc5d0 \uc801\ud600\uc788\ub294 \ub098\ub4e4\ubaa9\uc758 \ubc88\ud638\uac00 30\uc774\uace0 12\ubc88 \ub098\ub4e4\ubaa9\uc73c\ub85c \ub098\uac04\ub2e4\uba74, \uc694\uae08\uc740 18\uc6d0\uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\uace0\uc18d\ub3c4\ub85c \uc774\uc6a9 \uc694\uae08\uc740 \uc810\uc810 \ud68c\uc0ac\uac00 \uac10\ub2f9\ud560 \uc218 \uc5c6\ub294 \uc218\uc900\uae4c\uc9c0 \uce58\uc19f\uc558\uace0, \uc0c1\uadfc\uc774\ub294 \ud68d\uae30\uc801\uc778 \ubc29\ubc95\uc744 \uc0dd\uac01\ud574\ub0c8\ub2e4. \ubc14\ub85c, \uace0\uc18d\ub3c4\ub85c \uc911\uac04\uc5d0\uc11c \ub450 \uc6b4\uc804\uc0ac\uac00 \ub9cc\ub098\uc11c \ud2f0\ucf13\uc744 \uad50\ud658\ud558\ub294 \uac83\uc774\ub2e4. \uc774 \ubc29\ubc95\uc740 \uc11c\ub85c \uacbd\ub85c\uac00 \uacb9\uce58\uc9c0 \uc54a\ub354\ub77c\ub3c4 \uad50\ud658\ud560 \uc218 \uc788\uc73c\uba70, \ud2f0\ucf13\uc740 \uc5ec\ub7ec \ubc88 \uad50\ud658\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\ud558\uc9c0\ub9cc, \uc758\uc2ec\uc744 \ud53c\ud558\uae30 \uc704\ud574\uc11c \ud2f0\ucf13\uc5d0 \uc801\ud600\uc788\ub294 \ub098\ub4e4\ubaa9\uc758 \ubc88\ud638\uc640 \uac19\uc740 \ub098\ub4e4\ubaa9\uc73c\ub85c \ub098\uac08 \uc218\ub294 \uc5c6\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\r\n\t\uc6b4\uc804\uc0ac\ub07c\ub9ac \ud2f0\ucf13\uc744 \uc801\uc808\ud788 \uad50\ud658\ud588\uc744 \ub54c, \ub0b4\uc57c\ud558\ub294 \uace0\uc18d\ub3c4\ub85c \uc774\uc6a9 \uc694\uae08\uc758 \ucd5c\uc18c\uac12\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"\r\n\r\n<p>\r\n\t\uccab\uc9f8 \uc904\uc5d0 \ud2b8\ub7ed\uc758 \uc218 N\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; N &le; 100,000)<\/p>\r\n\r\n<p>\r\n\t\ub2e4\uc74c N\uac1c \uc904\uc5d0\ub294 \uac01 \ud2b8\ub7ed\uc774 \ub4e4\uc5b4\uc628 \ub098\ub4e4\ubaa9\uc758 \ubc88\ud638\uc640 \ub098\uac00\uc57c \ud558\ub294 \ub098\ub4e4\ubaa9\uc758 \ubc88\ud638\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc11c \uc8fc\uc5b4\uc9c4\ub2e4. \ub098\ub4e4\ubaa9\uc758 \ubc88\ud638\ub294 1\ubcf4\ub2e4 \ud06c\uac70\ub098 \uac19\uace0, 1,000,000\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\uc740 \uc790\uc5f0\uc218\uc774\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\ub450 \ud2b8\ub7ed\uc774 \uace0\uc18d\ub3c4\ub85c\ub85c \ub4e4\uc5b4\uc62c \ub54c \uc0ac\uc6a9\ud558\ub294 \ub098\ub4e4\ubaa9\uc758 \ubc88\ud638\ub098 \ub098\uac08 \ub54c \uc0ac\uc6a9\ud558\ub294 \ub098\ub4e4\ubaa9\uc758 \ubc88\ud638\uac00 \uac19\uc740 \uacbd\uc6b0\ub294 \uc5c6\ub2e4.<\/p>\r\n","output":"<p>\r\n\t\uc0c1\uadfc\uc774\ub124 \ud2b8\ub7ed \uc6b4\uc1a1 \ud68c\uc0ac\uac00 \ub0b4\uc57c\ud558\ub294 \uace0\uc18d\ub3c4\ub85c \uc774\uc6a9 \uc694\uae08\uc758 \ucd5c\uc18c\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4. \uc774 \uac12\uc740 32\ube44\ud2b8 \uc815\uc218 \ubc94\uc704\ub97c \ub118\uc5b4\uac08 \uc218 \uc788\uae30 \ub54c\ubb38\uc5d0, 64\ube44\ud2b8 \uc815\uc218(C\/C++: long long)\uc744 \uc0ac\uc6a9\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2984","problem_lang":"1","title":"CESTARINE","description":"<p>In a single day, N of Luka&#39;s trucks travel a specific highway. The highway has a number of exits and entrances. An exit with a particular number is in the same location as the entrance with that number.&nbsp;<\/p>\r\n\r\n<p>Upon entering the highway, a truck driver receives a ticket which indicates the entrance he used. When exiting, the driver pays a toll equal to the absolute difference of the entrance and exit numbers. For example, if a ticket says he used entrance 30, then exiting at exit 12 will cost him 18.&nbsp;<\/p>\r\n\r\n<p>Luka has figured out a way to save toll money that his company daily spends. Any two drivers can meet on the highway and exchange tickets, even if their routes don&#39;t overlap. Tickets can be exchanged an arbitrary number of times.&nbsp;<\/p>\r\n\r\n<p>However, a driver cannot use an exit if his ticket says he used the same entrance, since that would be suspicious.&nbsp;<\/p>\r\n\r\n<p>Write a program that calculates the least total amount of tolls that the drivers can achieve by exchanging tickets.&nbsp;<\/p>\r\n","input":"<p>The first line contains the integer N (1 &le; N &le; 100000), the number of trucks.&nbsp;<\/p>\r\n\r\n<p>Each of the following N lines contains two distinct integers between 1 and 1000000. These are in order the entrance and exit numbers of one truck.&nbsp;<\/p>\r\n\r\n<p>No two trucks will use the same highway entrance or the same exit.&nbsp;<\/p>\r\n","output":"<p>Output the least total amount of tolls Luka&#39;s company must pay.&nbsp;<\/p>\r\n\r\n<p>Note: use 64-bit integer types (long long in C\/C++, int64 in Pascal).&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]