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문제

JOI 상점가에서는 포인트 카드 서비스를 실시하고 있다. 각 포인트 카드에는 도장을 찍을 수 있는 칸이 총 2N개 있어, 상품을 구매하면 뽑기를 해서 결과에 따라 '당첨' 또는 '꽝' 도장이 찍힌다. 한 칸에 두 번 이상 도장을 찍을 수는 없다. 2N개 중 N개 이상의 칸에 당첨 도장이 찍힌 포인트 카드는 경품과 교환할 수 있다. 또, 한 칸에 찍힌 도장을 1엔을 내고 다른 도장으로 바꿀 수 있다.

JOI 군은 2N개 칸을 다 채운 포인트 카드를 M장 가지고 있다. i번째 포인트 카드에는 Ai개의 당첨 도장과, Bi개의 꽝 도장이 찍혀 있다.

JOI 군은 M-1개 이상의 경품을 가지려고 한다. 이에 필요한 비용의 최솟값을 구하라.

입력

입력은 M+1줄로 이루어진다.

첫 줄에는 2개의 정수 N, M(1 ≤ N ≤ 1000, 1 ≤ M ≤ 1000)이 공백을 사이에 두고 주어진다. 이는 포인트 카드에 2N개의 칸이 있고, JOI 군이 M장의 포인트 카드를 가지고 있음을 나타낸다.

다음 M개 줄 중 i번째(1 ≤ i ≤ M) 줄에는 각각 2개의 정수 Ai, Bi (0 ≤ Ai ≤ 2N, 0 ≤ Bi ≤ 2N, Ai + Bi = 2N)가 주어지며, 포인트 카드 i에 Ai개의 당첨 도장과 Bi개의 꽝 도장이 찍혀 있음을 나타낸다.

출력

JOI 군이 M-1개 이상의 경품을 얻기 위해 필요한 비용의 최솟값을 엔 단위로 한 줄로 출력하라.

예제 입력 1

4 5
1 7
6 2
3 5
4 4
0 8

예제 출력 1

4

예제 입력 2

5 4
5 5
8 2
3 7
8 2

예제 출력 2

0

힌트

예제 입출력 1에서, 포인트 카드 1의 꽝 도장 3개와 포인트 카드 3의 꽝 도장 1개를 당첨 도장으로 바꾸면, 4엔으로 5-1=4장의 카드가 경품과 교환 가능하게 되어, 이것이 최소 비용이다.

예제 입출력 2에서, 이미 4-1=3장의 카드가 경품과 교환 가능하므로 도장을 바꿀 필요가 없다.

[{"problem_id":"14471","problem_lang":"0","title":"\ud3ec\uc778\ud2b8 \uce74\ub4dc","description":"<p>JOI \uc0c1\uc810\uac00\uc5d0\uc11c\ub294 \ud3ec\uc778\ud2b8 \uce74\ub4dc \uc11c\ube44\uc2a4\ub97c \uc2e4\uc2dc\ud558\uace0 \uc788\ub2e4. \uac01 \ud3ec\uc778\ud2b8 \uce74\ub4dc\uc5d0\ub294 \ub3c4\uc7a5\uc744 \ucc0d\uc744 \uc218 \uc788\ub294 \uce78\uc774 \ucd1d 2N\uac1c \uc788\uc5b4, \uc0c1\ud488\uc744 \uad6c\ub9e4\ud558\uba74 \ubf51\uae30\ub97c \ud574\uc11c \uacb0\uacfc\uc5d0 \ub530\ub77c &#39;\ub2f9\ucca8&#39; \ub610\ub294 &#39;\uaf5d&#39; \ub3c4\uc7a5\uc774 \ucc0d\ud78c\ub2e4. \ud55c \uce78\uc5d0 \ub450 \ubc88 \uc774\uc0c1 \ub3c4\uc7a5\uc744 \ucc0d\uc744 \uc218\ub294 \uc5c6\ub2e4. 2N\uac1c \uc911 N\uac1c \uc774\uc0c1\uc758 \uce78\uc5d0 \ub2f9\ucca8 \ub3c4\uc7a5\uc774 \ucc0d\ud78c \ud3ec\uc778\ud2b8 \uce74\ub4dc\ub294 \uacbd\ud488\uacfc \uad50\ud658\ud560 \uc218 \uc788\ub2e4. \ub610, \ud55c \uce78\uc5d0 \ucc0d\ud78c \ub3c4\uc7a5\uc744 1\uc5d4\uc744 \ub0b4\uace0 \ub2e4\ub978 \ub3c4\uc7a5\uc73c\ub85c \ubc14\uafc0 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>JOI \uad70\uc740 2N\uac1c \uce78\uc744 \ub2e4 \ucc44\uc6b4 \ud3ec\uc778\ud2b8 \uce74\ub4dc\ub97c M\uc7a5 \uac00\uc9c0\uace0 \uc788\ub2e4. i\ubc88\uc9f8 \ud3ec\uc778\ud2b8 \uce74\ub4dc\uc5d0\ub294 A<sub>i<\/sub>\uac1c\uc758 \ub2f9\ucca8 \ub3c4\uc7a5\uacfc, B<sub>i<\/sub>\uac1c\uc758 \uaf5d \ub3c4\uc7a5\uc774 \ucc0d\ud600 \uc788\ub2e4.<\/p>\r\n\r\n<p>JOI \uad70\uc740 M-1\uac1c \uc774\uc0c1\uc758 \uacbd\ud488\uc744 \uac00\uc9c0\ub824\uace0 \ud55c\ub2e4. \uc774\uc5d0 \ud544\uc694\ud55c \ube44\uc6a9\uc758 \ucd5c\uc19f\uac12\uc744 \uad6c\ud558\ub77c.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 M+1\uc904\ub85c \uc774\ub8e8\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uccab \uc904\uc5d0\ub294 2\uac1c\uc758 \uc815\uc218 N, M(1 &le; N &le; 1000, 1 &le; M &le; 1000)\uc774 \uacf5\ubc31\uc744 \uc0ac\uc774\uc5d0 \ub450\uace0 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ub294 \ud3ec\uc778\ud2b8 \uce74\ub4dc\uc5d0 2N\uac1c\uc758 \uce78\uc774 \uc788\uace0, JOI \uad70\uc774 M\uc7a5\uc758 \ud3ec\uc778\ud2b8 \uce74\ub4dc\ub97c \uac00\uc9c0\uace0 \uc788\uc74c\uc744 \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c M\uac1c \uc904 \uc911 i\ubc88\uc9f8(1 &le; i &le; M) \uc904\uc5d0\ub294 \uac01\uac01 2\uac1c\uc758 \uc815\uc218 A<sub>i<\/sub>, B<sub>i<\/sub> (0 &le; A<sub>i<\/sub> &le; 2N, 0 &le; B<sub>i<\/sub> &le; 2N, A<sub>i<\/sub> + B<sub>i<\/sub> = 2N)\uac00 \uc8fc\uc5b4\uc9c0\uba70, \ud3ec\uc778\ud2b8 \uce74\ub4dc i\uc5d0 A<sub>i<\/sub>\uac1c\uc758 \ub2f9\ucca8 \ub3c4\uc7a5\uacfc B<sub>i<\/sub>\uac1c\uc758 \uaf5d \ub3c4\uc7a5\uc774 \ucc0d\ud600 \uc788\uc74c\uc744 \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n","output":"<p>JOI \uad70\uc774 M-1\uac1c \uc774\uc0c1\uc758 \uacbd\ud488\uc744 \uc5bb\uae30 \uc704\ud574 \ud544\uc694\ud55c \ube44\uc6a9\uc758 \ucd5c\uc19f\uac12\uc744 \uc5d4 \ub2e8\uc704\ub85c \ud55c \uc904\ub85c \ucd9c\ub825\ud558\ub77c.<\/p>\r\n","hint":"<p>\uc608\uc81c \uc785\ucd9c\ub825 1\uc5d0\uc11c, \ud3ec\uc778\ud2b8 \uce74\ub4dc 1\uc758 \uaf5d \ub3c4\uc7a5 3\uac1c\uc640 \ud3ec\uc778\ud2b8 \uce74\ub4dc 3\uc758 \uaf5d \ub3c4\uc7a5 1\uac1c\ub97c \ub2f9\ucca8 \ub3c4\uc7a5\uc73c\ub85c \ubc14\uafb8\uba74, 4\uc5d4\uc73c\ub85c 5-1=4\uc7a5\uc758 \uce74\ub4dc\uac00 \uacbd\ud488\uacfc \uad50\ud658 \uac00\ub2a5\ud558\uac8c \ub418\uc5b4, \uc774\uac83\uc774 \ucd5c\uc18c \ube44\uc6a9\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc608\uc81c \uc785\ucd9c\ub825 2\uc5d0\uc11c, \uc774\ubbf8 4-1=3\uc7a5\uc758 \uce74\ub4dc\uac00 \uacbd\ud488\uacfc \uad50\ud658 \uac00\ub2a5\ud558\ubbc0\ub85c \ub3c4\uc7a5\uc744 \ubc14\uafc0 \ud544\uc694\uac00 \uc5c6\ub2e4.<\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"14471","problem_lang":"2","title":"\u30dd\u30a4\u30f3\u30c8\u30ab\u30fc\u30c9 (Point Card)","description":"<p>JOI \u5546\u5e97\u8857\u3067\u306f\u30dd\u30a4\u30f3\u30c8\u30ab\u30fc\u30c9\u306e\u30b5\u30fc\u30d3\u30b9\u3092\u884c\u3063\u3066\u3044\u308b\uff0e\u5404\u30dd\u30a4\u30f3\u30c8\u30ab\u30fc\u30c9\u306b\u306f 2N \u500b\u306e\u30de\u30b9\u304c\u3042\u308b\uff0e\u5546\u54c1\u3092\u8cfc\u5165\u3059\u308b\u3068\uff0c\u304f\u3058\u3092\u5f15\u304f\u3053\u3068\u304c\u3067\u304d\uff0c\u7d50\u679c\u306b\u3088\u3063\u3066\u300c\u5f53\u305f\u308a\u300d\u304b\u300c\u306f\u305a\u308c\u300d\u306e\u5370\u304c\u30de\u30b9\u306b\u62bc\u3055\u308c\u308b\uff0e\u540c\u3058\u30de\u30b9\u306b\u5370\u304c 2 \u56de\u62bc\u3055\u308c\u308b\u3053\u3068\u306f\u306a\u3044\uff0e2N \u500b\u306e\u30de\u30b9\u306e\u3046\u3061 N \u500b\u4ee5\u4e0a\u306e\u30de\u30b9\u306b\u5f53\u305f\u308a\u306e\u5370\u304c\u66f8\u304b\u308c\u305f\u30dd\u30a4\u30f3\u30c8\u30ab\u30fc\u30c9\u306f\uff0c\u666f\u54c1\u3068\u4ea4\u63db\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e \u307e\u305f\uff0c\u30dd\u30a4\u30f3\u30c8\u30ab\u30fc\u30c9\u306e\u5370\u306f\uff0c1 \u30de\u30b9\u306b\u3064\u304d 1 \u5186\u3067\u66f8\u304d\u63db\u3048\u3066\u3082\u3089\u3046\u3053\u3068\u304c\u3067\u304d\u308b\uff0e<\/p>\r\n\r\n<p>JOI \u541b\u306f 2N \u500b\u306e\u30de\u30b9\u304c\u5168\u3066\u57cb\u307e\u3063\u3066\u3044\u308b\u30dd\u30a4\u30f3\u30c8\u30ab\u30fc\u30c9\u3092 M \u679a\u6301\u3063\u3066\u3044\u308b\uff0e\u30dd\u30a4\u30f3\u30c8\u30ab\u30fc\u30c9 i (1 \u2266 i \u2266 M) \u306b\u306f\uff0cA<sub>i<\/sub>&nbsp;\u500b\u306e\u5f53\u305f\u308a\u5370\u3068\uff0cB<sub>i<\/sub>&nbsp;\u500b\u306e\u306f\u305a\u308c\u5370\u304c\u62bc\u3055\u308c\u3066\u3044\u308b\uff0eJOI \u541b\u306f M - 1 \u500b\u4ee5\u4e0a\u306e\u666f\u54c1\u304c\u6b32\u3057\u3044\uff0e<\/p>\r\n\r\n<p>JOI \u541b\u304c M - 1 \u500b\u4ee5\u4e0a\u306e\u666f\u54c1\u3092\u5f97\u308b\u305f\u3081\u306b\u5fc5\u8981\u306a\u8cbb\u7528\u306e\u6700\u5c0f\u5024\u3092\u6c42\u3081\u3088\uff0e<\/p>\r\n","input":"<p>\u5165\u529b\u306f M + 1 \u884c\u304b\u3089\u306a\u308b\uff0e<\/p>\r\n\r\n<p>1 \u884c\u76ee\u306b\u306f\uff0c2 \u500b\u306e\u6574\u6570 N, M (1 \u2266 N \u2266 1000, 1 \u2266 M \u2266 1000) \u304c\u7a7a\u767d\u3092\u533a\u5207\u308a\u3068\u3057\u3066\u66f8\u304b\u308c\u3066\u3044\u308b\uff0e\u3053\u308c\u306f\uff0c\u30dd\u30a4\u30f3\u30c8\u30ab\u30fc\u30c9\u306b\u306f 2N \u500b\u306e\u30de\u30b9\u304c\u3042\u308a\uff0cJOI \u541b\u304c M \u679a\u306e\u30dd\u30a4\u30f3\u30c8\u30ab\u30fc\u30c9\u3092\u6301\u3063\u3066\u3044\u308b\u3053\u3068\u3092\u8868\u3059\uff0e<\/p>\r\n\r\n<p>\u7d9a\u304f M \u884c\u306e\u3046\u3061\u306e i \u884c\u76ee (1 \u2266 i \u2266 M) \u306b\u306f\uff0c\u305d\u308c\u305e\u308c 2 \u500b\u306e\u6574\u6570 A<sub>i<\/sub>, B<sub>i<\/sub>&nbsp;(0 \u2266 A<sub>i<\/sub>&nbsp;\u2266 2N, 0 \u2266 B<sub>i<\/sub>&nbsp;\u2266 2N, A<sub>i<\/sub>&nbsp;+ B<sub>i<\/sub>&nbsp;= 2N) \u304c\u66f8\u304b\u308c\u3066\u304a\u308a\uff0c\u30dd\u30a4\u30f3\u30c8\u30ab\u30fc\u30c9 i \u306b\u306f A<sub>i<\/sub>&nbsp;\u500b\u306e\u5f53\u305f\u308a\u5370\u3068 B<sub>i<\/sub>&nbsp;\u500b\u306e\u306f\u305a\u308c\u5370\u304c\u62bc\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u3092\u8868\u3059\uff0e<\/p>\r\n","output":"<p>JOI \u541b\u304c M - 1 \u500b\u4ee5\u4e0a\u306e\u666f\u54c1\u3092\u5f97\u308b\u305f\u3081\u306b\u5fc5\u8981\u306a\u8cbb\u7528\u306e\u6700\u5c0f\u5024\u3092 1 \u884c\u3067\u51fa\u529b\u305b\u3088\uff0e<\/p>\r\n","hint":"<p>\u5165\u529b\u4f8b 1 \u306b\u304a\u3044\u3066\u306f\uff0c\u30dd\u30a4\u30f3\u30c8\u30ab\u30fc\u30c9 1 \u306e\u306f\u305a\u308c\u5370\u3092 3 \u3064\u5f53\u305f\u308a\u5370\u306b\u66f8\u304d\u63db\u3048\u3066\u3082\u3089\u3044\uff0c\u30dd\u30a4\u30f3\u30c8\u30ab\u30fc\u30c9 3 \u306e\u306f\u305a\u308c\u5370\u3092 1 \u3064\u5f53\u305f\u308a\u5370\u306b\u66f8\u304d\u63db\u3048\u3066\u3082\u3089\u3046\u3068\uff0c4 \u5186\u3067 4 (= 5 - 1) \u679a\u306e\u30ab\u30fc\u30c9\u304c\u666f\u54c1\u3068\u4ea4\u63db\u53ef\u80fd\u306b\u306a\u308a\uff0c\u3053\u308c\u304c\u6700\u5c0f\u306e\u8cbb\u7528\u3067\u3042\u308b\uff0e<\/p>\r\n\r\n<p>\u5165\u529b\u4f8b 2 \u306b\u304a\u3044\u3066\u306f\uff0c\u65e2\u306b 3 (= 4 - 1) \u679a\u306e\u30ab\u30fc\u30c9\u304c\u666f\u54c1\u3068\u4ea4\u63db\u53ef\u80fd\u306a\u306e\u3067\uff0c\u66f8\u304d\u63db\u3048\u3066\u3082\u3089\u3046\u5fc5\u8981\u306a\u3044\uff0e<\/p>\r\n\r\n<p>\u203b\u5404\u5165\u51fa\u529b\u4f8b\u306e\u30c7\u30fc\u30bf\u306f\uff0c\u53f3\u30af\u30ea\u30c3\u30af\u7b49\u306b\u3088\u308a\u30d5\u30a1\u30a4\u30eb\u306b\u4fdd\u5b58\u3057\u3066\u5229\u7528\u53ef\u80fd\u3067\u3059\uff0e<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"Japanese"}]

출처

Olympiad > Japanese Olympiad in Informatics > Japanese Olympiad in Informatics Qualification Round > JOI 2016/2017 예선 2번

  • 문제의 오타를 찾은 사람: index
  • 문제를 번역한 사람: paulsohn