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문제

스케줄링 최적화 회사인 SOPT 에 완료해야 할 n개의 작업 t1, t2, ..., tn 이 있다. SOPT 회사는 두 대의 머신 AB 를 보유하고 있다. 각 작업 ti를 완료하기 위해 SOPT 는 머신 A 와 B 둘 중에 오직 하나를 선택할 수 있다. 작업 ti를 완료하기 위해 머신 A를 선택하면 ai시간이 걸리고 머신 B를 선택하면 bi 시간이 걸린다. 각 머신은 어느 순간에 최대 하나의 작업만 수행할 수 있으며, 한 작업이 시작되면 그 작업을 완료하기 전까지 다른 작업을 그 머신에서 수행할 수 없다. SOPT 는 모든 작업을 완료하기 위한 최소의 완료 시간을 구하고자 한다.

예를 들어, 세 개의 작업이 t1, t2, t3가 주어져 있고 a1 = 2, b1 = 3, a2 = 5, b2 = 3, a3 = 2, b3 = 7라고 하자. 완료 시간을 최소화하기 위해서는 작업 t1, t3는 머신 A에, 작업 t2는 머신 B에 할당한다. 머신 A는 작업 t1, t3를 완료하는데 2 + 2 = 4 시간이 걸리고 머신 B는 작업 t2를 완료하는데 3 시간이 걸린다. 따라서 최소 완료 시간은 4 시간이 된다. n개의 작업 t1t2, ..., tn 과 각 머신에서 각 작업들을 수행하는 데 걸리는 시간들이 주어질 때, 모든 작업들을 완료하기 위해 걸리는 시간의 최솟값을 구하는 프로그램을 작성하시오.

입력

입력은 표준입력을 사용한다. 첫 번째 줄에 작업의 개수를 나타내는 양의 정수 n (1 ≤ n ≤ 250)이 주어진다. 다음 n개의 줄에서 i번째 줄에는 두 개의 정수 ai, bi (1 ≤ ai, bi ≤ 250)가 주어진다. 여기서 aibi는 각각 작업 ti를 머신 AB에서 완료하는데 걸리는 시간이다.

출력

출력은 표준출력을 사용한다. 모든 작업 t1, t2, ..., tn을 완료하기 위한 최소의 완료시간을 한 줄에 출력한다.

예제 입력 1

3
2 3
5 3
2 7

예제 출력 1

4

예제 입력 2

3
9 2
10 4
5 2

예제 출력 2

6
[{"problem_id":"17528","problem_lang":"0","title":"Two Machines","description":"<p>\uc2a4\ucf00\uc904\ub9c1 \ucd5c\uc801\ud654 \ud68c\uc0ac\uc778 SOPT \uc5d0 \uc644\ub8cc\ud574\uc57c \ud560 <em>n<\/em>\uac1c\uc758 \uc791\uc5c5 <em>t<\/em><sub>1<\/sub>, <em>t<\/em><sub>2<\/sub>, ..., <em>t<sub>n<\/sub><\/em>&nbsp;\uc774 \uc788\ub2e4. SOPT \ud68c\uc0ac\ub294 \ub450 \ub300\uc758 \uba38\uc2e0 <em>A<\/em> \uc640 <em>B<\/em> \ub97c \ubcf4\uc720\ud558\uace0 \uc788\ub2e4. \uac01 \uc791\uc5c5 <em>t<sub>i<\/sub><\/em>\ub97c \uc644\ub8cc\ud558\uae30 \uc704\ud574 SOPT \ub294 \uba38\uc2e0 <em>A<\/em>&nbsp;\uc640 <em>B<\/em>&nbsp;\ub458 \uc911\uc5d0 \uc624\uc9c1 \ud558\ub098\ub97c \uc120\ud0dd\ud560 \uc218 \uc788\ub2e4. \uc791\uc5c5 <em>t<sub>i<\/sub><\/em>\ub97c \uc644\ub8cc\ud558\uae30 \uc704\ud574 \uba38\uc2e0 <em>A<\/em>\ub97c \uc120\ud0dd\ud558\uba74 <em>a<sub>i<\/sub><\/em>\uc2dc\uac04\uc774 \uac78\ub9ac\uace0 \uba38\uc2e0 <em>B<\/em>\ub97c \uc120\ud0dd\ud558\uba74 <em>b<sub>i<\/sub><\/em>&nbsp;\uc2dc\uac04\uc774 \uac78\ub9b0\ub2e4. \uac01 \uba38\uc2e0\uc740 \uc5b4\ub290 \uc21c\uac04\uc5d0 \ucd5c\ub300 \ud558\ub098\uc758 \uc791\uc5c5\ub9cc \uc218\ud589\ud560 \uc218 \uc788\uc73c\uba70, \ud55c \uc791\uc5c5\uc774 \uc2dc\uc791\ub418\uba74 \uadf8 \uc791\uc5c5\uc744 \uc644\ub8cc\ud558\uae30 \uc804\uae4c\uc9c0 \ub2e4\ub978 \uc791\uc5c5\uc744 \uadf8 \uba38\uc2e0\uc5d0\uc11c \uc218\ud589\ud560 \uc218 \uc5c6\ub2e4. SOPT \ub294 \ubaa8\ub4e0 \uc791\uc5c5\uc744 \uc644\ub8cc\ud558\uae30 \uc704\ud55c \ucd5c\uc18c\uc758 \uc644\ub8cc \uc2dc\uac04\uc744 \uad6c\ud558\uace0\uc790 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, \uc138 \uac1c\uc758 \uc791\uc5c5\uc774 <em>t<\/em><sub>1<\/sub>, <em>t<\/em><sub>2<\/sub>, <em>t<\/em><sub>3<\/sub>\uac00 \uc8fc\uc5b4\uc838 \uc788\uace0 <em>a<\/em><sub>1<\/sub>&nbsp;= 2, <em>b<\/em><sub>1<\/sub> = 3, <em>a<\/em><sub>2<\/sub>&nbsp;= 5, <em>b<\/em><sub>2<\/sub>&nbsp;= 3, <em>a<\/em><sub>3<\/sub>&nbsp;= 2, <em>b<\/em><sub>3<\/sub>&nbsp;= 7\ub77c\uace0 \ud558\uc790. \uc644\ub8cc \uc2dc\uac04\uc744 \ucd5c\uc18c\ud654\ud558\uae30 \uc704\ud574\uc11c\ub294 \uc791\uc5c5 <em>t<\/em><sub>1<\/sub>, <em>t<\/em><sub>3<\/sub>\ub294 \uba38\uc2e0 <em>A<\/em>\uc5d0, \uc791\uc5c5 <em>t<\/em><sub>2<\/sub>\ub294 \uba38\uc2e0 <em>B<\/em>\uc5d0 \ud560\ub2f9\ud55c\ub2e4. \uba38\uc2e0 <em>A<\/em>\ub294 \uc791\uc5c5 <em>t<\/em><sub>1<\/sub>, <em>t<\/em><sub>3<\/sub>\ub97c \uc644\ub8cc\ud558\ub294\ub370 2 + 2 = 4 \uc2dc\uac04\uc774 \uac78\ub9ac\uace0 \uba38\uc2e0 <em>B<\/em>\ub294 \uc791\uc5c5 <em>t<\/em><sub>2<\/sub>\ub97c \uc644\ub8cc\ud558\ub294\ub370 3 \uc2dc\uac04\uc774 \uac78\ub9b0\ub2e4. \ub530\ub77c\uc11c \ucd5c\uc18c \uc644\ub8cc \uc2dc\uac04\uc740 4 \uc2dc\uac04\uc774 \ub41c\ub2e4. <em>n<\/em>\uac1c\uc758 \uc791\uc5c5 <em>t<\/em><sub>1<\/sub>,&nbsp;<em>t<\/em><sub>2<\/sub>, ...,&nbsp;<em>t<sub>n<\/sub><\/em>&nbsp;\uacfc \uac01 \uba38\uc2e0\uc5d0\uc11c \uac01 \uc791\uc5c5\ub4e4\uc744 \uc218\ud589\ud558\ub294 \ub370 \uac78\ub9ac\ub294 \uc2dc\uac04\ub4e4\uc774 \uc8fc\uc5b4\uc9c8 \ub54c, \ubaa8\ub4e0 \uc791\uc5c5\ub4e4\uc744 \uc644\ub8cc\ud558\uae30 \uc704\ud574 \uac78\ub9ac\ub294 \uc2dc\uac04\uc758 \ucd5c\uc19f\uac12\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \ud45c\uc900\uc785\ub825\uc744 \uc0ac\uc6a9\ud55c\ub2e4. \uccab \ubc88\uc9f8 \uc904\uc5d0 \uc791\uc5c5\uc758 \uac1c\uc218\ub97c \ub098\ud0c0\ub0b4\ub294 \uc591\uc758 \uc815\uc218 <em>n<\/em>&nbsp;(1 &le; <em>n<\/em>&nbsp;&le; 250)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ub2e4\uc74c <em>n<\/em>\uac1c\uc758 \uc904\uc5d0\uc11c <em>i<\/em>\ubc88\uc9f8 \uc904\uc5d0\ub294 \ub450 \uac1c\uc758 \uc815\uc218 <em>a<sub>i<\/sub><\/em>, <em>b<sub>i<\/sub><\/em> (1 &le; <em>a<sub>i<\/sub><\/em>, <em>b<sub>i<\/sub><\/em>&nbsp;&le; 250)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc5ec\uae30\uc11c&nbsp;<em>a<sub>i<\/sub><\/em>\uc640 <em>b<sub>i<\/sub><\/em>\ub294 \uac01\uac01 \uc791\uc5c5 <em>t<sub>i<\/sub><\/em>\ub97c \uba38\uc2e0 <em>A<\/em>\uc640 <em>B<\/em>\uc5d0\uc11c \uc644\ub8cc\ud558\ub294\ub370 \uac78\ub9ac\ub294 \uc2dc\uac04\uc774\ub2e4.<\/p>\r\n","output":"<p>\ucd9c\ub825\uc740 \ud45c\uc900\ucd9c\ub825\uc744 \uc0ac\uc6a9\ud55c\ub2e4. \ubaa8\ub4e0 \uc791\uc5c5 <em>t<\/em><sub>1<\/sub>, <em>t<\/em><sub>2<\/sub>, ..., <em>t<sub>n<\/sub><\/em>\uc744 \uc644\ub8cc\ud558\uae30 \uc704\ud55c \ucd5c\uc18c\uc758 \uc644\ub8cc\uc2dc\uac04\uc744 \ud55c \uc904\uc5d0 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"17528","problem_lang":"1","title":"Two Machines","description":"<p>A scheduling company SOPT has tasks <em>t<\/em><sub>1<\/sub>, <em>t<\/em><sub>2<\/sub>, ..., <em>t<sub>n<\/sub><\/em> to complete. The company has two super machines <em>A<\/em>&nbsp;and <em>B<\/em>. To complete a task <em>t<sub>i<\/sub><\/em>, SOPT can choose only one of <em>A<\/em>&nbsp;and <em>B<\/em>. It takes <em>a<sub>i<\/sub><\/em>&nbsp;and <em>b<sub>i<\/sub><\/em>&nbsp;hours to complete the task&nbsp;<em>t<sub>i<\/sub><\/em>&nbsp;on the machines <em>A<\/em> and <em>B<\/em>, respectively. A machine can run at most one task at any time, and if it starts to run a task <em>t<sub>i<\/sub><\/em>&nbsp;then it cannot run another task <em>t<sub>j<\/sub><\/em>&nbsp;until the machine completes <em>t<sub>i<\/sub><\/em>. SOPT wants to minimize the completion time for all tasks.<\/p>\r\n\r\n<p>For example, we have three tasks <em>t<\/em><sub>1<\/sub>, <em>t<\/em><sub>2<\/sub>, and <em>t<\/em><sub>3<\/sub> with <em>a<\/em><sub>1<\/sub>&nbsp;= 2, <em>b<\/em><sub>1<\/sub> = 3, <em>a<\/em><sub>2<\/sub> = 5, <em>b<\/em><sub>2<\/sub> = 3, <em>a<\/em><sub>3<\/sub>&nbsp;= 2, and <em>b<\/em><sub>3<\/sub> = 7. The best way to minimize the completion time is to assign two tasks <em>t<\/em><sub>1<\/sub>&nbsp;and <em>t<\/em><sub>3<\/sub>&nbsp;to the machine <em>A<\/em> and to assign the other task <em>t<\/em><sub>2<\/sub> to the machine <em>B<\/em>. Then <em>A<\/em> needs 2 + 2 = 4 hours to complete <em>t<\/em><sub>1<\/sub>&nbsp;and <em>t<\/em><sub>3<\/sub>, and <em>B<\/em> needs 3 hours to complete <em>t<\/em><sub>2<\/sub>, so the minimum completion time is 4 hours.<\/p>\r\n\r\n<p>Given <em>n<\/em> tasks and the times to complete the tasks on machines <em>A<\/em>&nbsp;and <em>B<\/em>, write a program to output the minimum completion time to complete all tasks.<\/p>\r\n","input":"<p>Your program is to read from standard input. The input starts with a line containing one integer, <em>n<\/em> (1 &le; <em>n<\/em> &le; 250), where <em>n<\/em> is the number of tasks. In the following <em>n<\/em> lines, the <em>i<\/em>-th line contains two integers <em>a<sub>i<\/sub><\/em>&nbsp;and <em>b<sub>i<\/sub><\/em>&nbsp;(1 &le; <em>a<sub>i<\/sub><\/em>, <em>b<sub>i<\/sub><\/em>&nbsp;&le; 250) where <em>a<sub>i<\/sub><\/em> and <em>b<sub>i<\/sub><\/em> denote the time to complete the task <em>t<sub>i<\/sub><\/em>&nbsp;on the machines <em>A<\/em> and <em>B<\/em>, respectively.<\/p>\r\n","output":"<p>Your program is to write to standard output. Print exactly one line. The line should contain the minimum completion time to complete all tasks.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English"}]