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문제

상덕이와 희원이는 동전 게임을 하면서 시간을 보낸다. 동전 게임은 동전 N개를 가지고 하는 게임이고, 규칙은 다음과 같다.

  1. 상덕이가 먼저 게임을 하고, 그 다음엔 희원이, 그 다음에 상덕이, 희원이 순서대로 게임을 한다. 순서대로 첫 번째 턴, 두 번째 턴, 세 번째 턴, ...
  2. 상덕이는 첫 번째 턴에서 가져갈 수 있는 동전의 개수는 1보다 크거나 같고, N보다 작거나 같다.
  3. 그 다음 턴부터는 동전을 이전 턴에서 그 사람이 가져간 동전 개수의 최대 2배만큼 가져갈 수 있다. (동전을 적어도 1개는 가져가야 한다)
  4. 이렇게 플레이를 하다가 마지막 동전을 가져가는 사람이 이긴다.

상덕이와 희원이가 항상 최적의 방법으로 게임을 한다. 이 말은 어떤 상황에서 플레이어 A가 B를 항상 이길 수 있다면, A가 항상 이긴다는 것이다.)

이때, 상덕이가 이기기 위해서는 첫 번째 턴에서 동전을 몇 개 가져가야 하는지를 구하는 프로그램을 작성하면 된다. 이러한 동전의 개수가 여러 개 나올 수 있는데, 그 때는 가장 적은 개수를 출력하면 된다.

입력

첫째 줄에 동전의 개수 N이 주어진다. (2 ≤ N ≤ 1015)

출력

첫째 줄에 상덕이가 이기기 위해서 가져가야 하는 동전 개수의 최솟값을 출력한다.

예제 입력 1

4

예제 출력 1

1

힌트

동전의 개수가 4개일 때, 상덕이가 첫 번째 턴에서 가져갈 수 있는 동전의 경우의 수는 1, 2, 3, 4개이다. 만약 4개를 가져가게 된다면 상덕이는 항상 이기게 된다. 하지만, 이것은 최솟값이 아니다. 상덕이가 첫 번째 턴에서 동전을 1개 가져갔다고 생각해보자. 그럼 이제 동전은 3개가 남고, 희원이는 동전을 많아야 2개만 가져갈 수 있기 때문에 절대 이길 수 없게 된다. (문제의 3번 조건 때문에 희원이는 동전을 1*2개까지 가져갈 수 있다) 희원이가 동전을 1개를 가져가던, 2개를 가져가던 상덕이는 다음 턴에서 남은 동전을 모두 가져갈 수 있기 때문에 상덕이가 첫 번째 턴에서 동전을 1개 가져가면 항상 이기게 된다. 따라서 정답은 1이다.

[{"problem_id":"2862","problem_lang":"0","title":"\uc218\ud559 \uac8c\uc784","description":"<p>\uc0c1\ub355\uc774\uc640 \ud76c\uc6d0\uc774\ub294 \ub3d9\uc804 \uac8c\uc784\uc744 \ud558\uba74\uc11c \uc2dc\uac04\uc744 \ubcf4\ub0b8\ub2e4. \ub3d9\uc804 \uac8c\uc784\uc740 \ub3d9\uc804 N\uac1c\ub97c \uac00\uc9c0\uace0 \ud558\ub294 \uac8c\uc784\uc774\uace0, \uaddc\uce59\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<ol>\r\n\t<li>\uc0c1\ub355\uc774\uac00 \uba3c\uc800 \uac8c\uc784\uc744 \ud558\uace0, \uadf8 \ub2e4\uc74c\uc5d4 \ud76c\uc6d0\uc774, \uadf8 \ub2e4\uc74c\uc5d0 \uc0c1\ub355\uc774, \ud76c\uc6d0\uc774 \uc21c\uc11c\ub300\ub85c \uac8c\uc784\uc744 \ud55c\ub2e4. \uc21c\uc11c\ub300\ub85c \uccab \ubc88\uc9f8 \ud134, \ub450 \ubc88\uc9f8 \ud134, \uc138 \ubc88\uc9f8 \ud134, ...<\/li>\r\n\t<li>\uc0c1\ub355\uc774\ub294 \uccab \ubc88\uc9f8 \ud134\uc5d0\uc11c \uac00\uc838\uac08 \uc218 \uc788\ub294 \ub3d9\uc804\uc758 \uac1c\uc218\ub294 1\ubcf4\ub2e4 \ud06c\uac70\ub098 \uac19\uace0, N\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\ub2e4.<\/li>\r\n\t<li>\uadf8 \ub2e4\uc74c \ud134\ubd80\ud130\ub294 \ub3d9\uc804\uc744&nbsp;\uc774\uc804 \ud134\uc5d0\uc11c \uadf8 \uc0ac\ub78c\uc774 \uac00\uc838\uac04 \ub3d9\uc804 \uac1c\uc218\uc758 \ucd5c\ub300 2\ubc30\ub9cc\ud07c \uac00\uc838\uac08 \uc218 \uc788\ub2e4. (\ub3d9\uc804\uc744 \uc801\uc5b4\ub3c4 1\uac1c\ub294 \uac00\uc838\uac00\uc57c \ud55c\ub2e4)<\/li>\r\n\t<li>\uc774\ub807\uac8c \ud50c\ub808\uc774\ub97c \ud558\ub2e4\uac00 \ub9c8\uc9c0\ub9c9 \ub3d9\uc804\uc744 \uac00\uc838\uac00\ub294 \uc0ac\ub78c\uc774 \uc774\uae34\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p>\uc0c1\ub355\uc774\uc640 \ud76c\uc6d0\uc774\uac00 \ud56d\uc0c1 \ucd5c\uc801\uc758 \ubc29\ubc95\uc73c\ub85c \uac8c\uc784\uc744 \ud55c\ub2e4. \uc774 \ub9d0\uc740 \uc5b4\ub5a4 \uc0c1\ud669\uc5d0\uc11c \ud50c\ub808\uc774\uc5b4 A\uac00 B\ub97c \ud56d\uc0c1 \uc774\uae38 \uc218 \uc788\ub2e4\uba74, A\uac00 \ud56d\uc0c1 \uc774\uae34\ub2e4\ub294 \uac83\uc774\ub2e4.)<\/p>\r\n\r\n<p>\uc774\ub54c, \uc0c1\ub355\uc774\uac00 \uc774\uae30\uae30 \uc704\ud574\uc11c\ub294 \uccab \ubc88\uc9f8 \ud134\uc5d0\uc11c \ub3d9\uc804\uc744 \uba87 \uac1c \uac00\uc838\uac00\uc57c \ud558\ub294\uc9c0\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uba74 \ub41c\ub2e4. \uc774\ub7ec\ud55c \ub3d9\uc804\uc758 \uac1c\uc218\uac00 \uc5ec\ub7ec \uac1c \ub098\uc62c \uc218 \uc788\ub294\ub370, \uadf8 \ub54c\ub294 \uac00\uc7a5 \uc801\uc740 \uac1c\uc218\ub97c \ucd9c\ub825\ud558\uba74 \ub41c\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ub3d9\uc804\uc758 \uac1c\uc218 N\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (2 &le; N &le; 10<sup>15<\/sup>)<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc0c1\ub355\uc774\uac00 \uc774\uae30\uae30 \uc704\ud574\uc11c \uac00\uc838\uac00\uc57c \ud558\ub294 \ub3d9\uc804 \uac1c\uc218\uc758 \ucd5c\uc19f\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\ub3d9\uc804\uc758 \uac1c\uc218\uac00 4\uac1c\uc77c \ub54c, \uc0c1\ub355\uc774\uac00 \uccab \ubc88\uc9f8 \ud134\uc5d0\uc11c \uac00\uc838\uac08 \uc218 \uc788\ub294 \ub3d9\uc804\uc758 \uacbd\uc6b0\uc758 \uc218\ub294 1, 2, 3, 4\uac1c\uc774\ub2e4. \ub9cc\uc57d 4\uac1c\ub97c \uac00\uc838\uac00\uac8c \ub41c\ub2e4\uba74 \uc0c1\ub355\uc774\ub294 \ud56d\uc0c1 \uc774\uae30\uac8c \ub41c\ub2e4. \ud558\uc9c0\ub9cc, \uc774\uac83\uc740 \ucd5c\uc19f\uac12\uc774 \uc544\ub2c8\ub2e4. \uc0c1\ub355\uc774\uac00 \uccab \ubc88\uc9f8 \ud134\uc5d0\uc11c \ub3d9\uc804\uc744 1\uac1c \uac00\uc838\uac14\ub2e4\uace0 \uc0dd\uac01\ud574\ubcf4\uc790. \uadf8\ub7fc \uc774\uc81c \ub3d9\uc804\uc740 3\uac1c\uac00 \ub0a8\uace0, \ud76c\uc6d0\uc774\ub294 \ub3d9\uc804\uc744 \ub9ce\uc544\uc57c 2\uac1c\ub9cc \uac00\uc838\uac08 \uc218 \uc788\uae30 \ub54c\ubb38\uc5d0 \uc808\ub300 \uc774\uae38 \uc218 \uc5c6\uac8c \ub41c\ub2e4. (\ubb38\uc81c\uc758 3\ubc88 \uc870\uac74 \ub54c\ubb38\uc5d0 \ud76c\uc6d0\uc774\ub294 \ub3d9\uc804\uc744 1*2\uac1c\uae4c\uc9c0 \uac00\uc838\uac08 \uc218 \uc788\ub2e4) \ud76c\uc6d0\uc774\uac00 \ub3d9\uc804\uc744 1\uac1c\ub97c \uac00\uc838\uac00\ub358, 2\uac1c\ub97c \uac00\uc838\uac00\ub358 \uc0c1\ub355\uc774\ub294 \ub2e4\uc74c \ud134\uc5d0\uc11c \ub0a8\uc740 \ub3d9\uc804\uc744 \ubaa8\ub450 \uac00\uc838\uac08 \uc218 \uc788\uae30 \ub54c\ubb38\uc5d0 \uc0c1\ub355\uc774\uac00 \uccab \ubc88\uc9f8 \ud134\uc5d0\uc11c \ub3d9\uc804\uc744 1\uac1c \uac00\uc838\uac00\uba74 \ud56d\uc0c1 \uc774\uae30\uac8c \ub41c\ub2e4. \ub530\ub77c\uc11c \uc815\ub2f5\uc740 1\uc774\ub2e4.<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2862","problem_lang":"1","title":"HRPA","description":"<p>Mirko and Slavko&rsquo;s favourite pastime is competing against each other in mathematical games. This time they took a heap of N pebbles and settled on the following rules:&nbsp;<\/p>\r\n\r\n<ol>\r\n\t<li>Mirko is the first to play, then Slavko, then Mirko again, then Slavko and so on;&nbsp;<\/li>\r\n\t<li>Mirko can take any number of pebbles (between 1 and N, inclusive) from the heap during his first move;&nbsp;<\/li>\r\n\t<li>In each of the following turns the current player must take at least 1 pebble and is allowed to take at most double the amount of pebbles taken during the previous turn by the other player; naturally, one cannot take more pebbles than the remaining amount in the heap;&nbsp;<\/li>\r\n\t<li>The player who takes the last pebble is the winner.<\/li>\r\n<\/ol>\r\n\r\n<p>Both Mirko and Slavko play optimally (if it is possible for one player to beat the other, that player will always win). We need to find the minimum number of pebbles that Mirko must take during his first turn such that he is guaranteed to win the game.&nbsp;<\/p>\r\n","input":"<p>The first and only line of input contains the positive integer N (2 &le; N &le; 10<sup>15<\/sup>), the number of pebbles in the starting heap.&nbsp;<\/p>\r\n","output":"<p>The first and only line of output must contain the required minimum number of pebbles that Mirko needs to remove during his first turn.&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

Contest > Croatian Open Competition in Informatics > COCI 2010/2011 > Contest #4 6번