시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 128 MB 60 37 21 63.636%

문제

해빈시의 공원에는 화장실이 두 개가 있다. 그런데 그 중 하나가 얼마전에 고장났다. 이제 남은 건 한 개 뿐이다....

문제는 해빈이는 당장 화장실이 가고 싶은데, 화장실 앞의 줄이 매우 길다는 것이다!

고통을 잊기 위해 해빈이는 절망적인 줄을 쳐다보며 아래와 같은 문제를 풀기 시작했다.

화장실 사용료는 50원이다. 줄에 서 있는 사람들 중 반은 50원 동전을 가지고 있고, 나머지 반은 100원 동전만 가지고 있다.

화장실을 개장할 때, 관리인은 거슬러 줄 동전을 가지고 있지 않다.

100원 동전만 가진 사람에게는 50원 동전을 거슬러 줘야 한다. (이 경우, 50원 동전을 가진 사람이 먼저 등어가면서 지불한 동전을 거스름돈으로 사용한다)

사람들의 위치를 적절히 바꿔서 관리인의 거스름돈이 항상 모자라지 않게 하는 방법의 수를 구하라. 이 때, 일부 사람들은 절대로 자리를 바꾸지 않는다. (뒤쪽, 앞쪽 모두 다)

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다.

각 테스트 케이스는 길이가 n (1 ≤ n ≤ 1,000) 인 문자열 한 줄로 이루어져 있으며, 50원 동전을 가지고 있으면서 자리를 바꾸길 원치 않는 사람을 나타내는 '('와 100원 동전을 가지고 있으면서 자리를 바꾸길 원치 않는 사람을 나타내는 ')', 자리를 바꿔도 되는 사람을 나타내는 '.'으로 이루어져 있다.

'('와 ')'의 개수는 각각 n/2개 이하이고, n은 항상 짝수이다.

출력

각 테스트 케이스에 대해 문제의 조건을 지키며 자리를 바꿀 수 있는 방법의 수를 출력하라. 단, 문제의 답이 매우 커질 수 있으므로 마지막 여섯자리만 출력한다.

예제 입력 1

....
.(..
)...
.....)......................

예제 출력 1

2
1
0
68484
[{"problem_id":"9278","problem_lang":"0","title":"\uc808\ub9dd\uc801\uc778 \uc904","description":"<p>\ud574\ube48\uc2dc\uc758 \uacf5\uc6d0\uc5d0\ub294 \ud654\uc7a5\uc2e4\uc774 \ub450 \uac1c\uac00 \uc788\ub2e4. \uadf8\ub7f0\ub370 \uadf8 \uc911 \ud558\ub098\uac00 \uc5bc\ub9c8\uc804\uc5d0 \uace0\uc7a5\ub0ac\ub2e4. \uc774\uc81c \ub0a8\uc740 \uac74 \ud55c \uac1c \ubfd0\uc774\ub2e4....<\/p>\r\n\r\n<p>\ubb38\uc81c\ub294 \ud574\ube48\uc774\ub294 \ub2f9\uc7a5 \ud654\uc7a5\uc2e4\uc774 \uac00\uace0 \uc2f6\uc740\ub370, \ud654\uc7a5\uc2e4 \uc55e\uc758 \uc904\uc774 \ub9e4\uc6b0 \uae38\ub2e4\ub294 \uac83\uc774\ub2e4!<\/p>\r\n\r\n<p>\uace0\ud1b5\uc744 \uc78a\uae30 \uc704\ud574 \ud574\ube48\uc774\ub294 \uc808\ub9dd\uc801\uc778 \uc904\uc744 \uccd0\ub2e4\ubcf4\uba70 \uc544\ub798\uc640 \uac19\uc740 \ubb38\uc81c\ub97c \ud480\uae30 \uc2dc\uc791\ud588\ub2e4.<\/p>\r\n\r\n<blockquote>\r\n<p>\ud654\uc7a5\uc2e4 \uc0ac\uc6a9\ub8cc\ub294 50\uc6d0\uc774\ub2e4. \uc904\uc5d0 \uc11c \uc788\ub294 \uc0ac\ub78c\ub4e4 \uc911 \ubc18\uc740 50\uc6d0 \ub3d9\uc804\uc744 \uac00\uc9c0\uace0 \uc788\uace0, \ub098\uba38\uc9c0 \ubc18\uc740 100\uc6d0 \ub3d9\uc804\ub9cc \uac00\uc9c0\uace0 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ud654\uc7a5\uc2e4\uc744 \uac1c\uc7a5\ud560 \ub54c, \uad00\ub9ac\uc778\uc740 \uac70\uc2ac\ub7ec \uc904 \ub3d9\uc804\uc744 \uac00\uc9c0\uace0 \uc788\uc9c0 \uc54a\ub2e4.<\/p>\r\n\r\n<p>100\uc6d0 \ub3d9\uc804\ub9cc \uac00\uc9c4 \uc0ac\ub78c\uc5d0\uac8c\ub294 50\uc6d0 \ub3d9\uc804\uc744 \uac70\uc2ac\ub7ec \uc918\uc57c \ud55c\ub2e4. (\uc774 \uacbd\uc6b0, 50\uc6d0 \ub3d9\uc804\uc744 \uac00\uc9c4 \uc0ac\ub78c\uc774 \uba3c\uc800 \ub4f1\uc5b4\uac00\uba74\uc11c \uc9c0\ubd88\ud55c \ub3d9\uc804\uc744 \uac70\uc2a4\ub984\ub3c8\uc73c\ub85c \uc0ac\uc6a9\ud55c\ub2e4)<\/p>\r\n\r\n<p>\uc0ac\ub78c\ub4e4\uc758 \uc704\uce58\ub97c \uc801\uc808\ud788 \ubc14\uafd4\uc11c \uad00\ub9ac\uc778\uc758 \uac70\uc2a4\ub984\ub3c8\uc774 \ud56d\uc0c1 \ubaa8\uc790\ub77c\uc9c0 \uc54a\uac8c \ud558\ub294 \ubc29\ubc95\uc758 \uc218\ub97c \uad6c\ud558\ub77c. \uc774 \ub54c, \uc77c\ubd80 \uc0ac\ub78c\ub4e4\uc740 \uc808\ub300\ub85c \uc790\ub9ac\ub97c \ubc14\uafb8\uc9c0 \uc54a\ub294\ub2e4. (\ub4a4\ucabd, \uc55e\ucabd \ubaa8\ub450 \ub2e4)<\/p>\r\n<\/blockquote>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \uae38\uc774\uac00 n (1 &le; n &le; 1,000) \uc778 \ubb38\uc790\uc5f4 \ud55c \uc904\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uc73c\uba70, 50\uc6d0 \ub3d9\uc804\uc744 \uac00\uc9c0\uace0 \uc788\uc73c\uba74\uc11c \uc790\ub9ac\ub97c \ubc14\uafb8\uae38 \uc6d0\uce58 \uc54a\ub294 \uc0ac\ub78c\uc744 \ub098\ud0c0\ub0b4\ub294 &#39;(&#39;\uc640 100\uc6d0 \ub3d9\uc804\uc744 \uac00\uc9c0\uace0 \uc788\uc73c\uba74\uc11c \uc790\ub9ac\ub97c \ubc14\uafb8\uae38 \uc6d0\uce58 \uc54a\ub294 \uc0ac\ub78c\uc744 \ub098\ud0c0\ub0b4\ub294 &#39;)&#39;, \uc790\ub9ac\ub97c \ubc14\uafd4\ub3c4 \ub418\ub294 \uc0ac\ub78c\uc744 \ub098\ud0c0\ub0b4\ub294 &#39;.&#39;\uc73c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>&#39;(&#39;\uc640 &#39;)&#39;\uc758 \uac1c\uc218\ub294 \uac01\uac01 n\/2\uac1c \uc774\ud558\uc774\uace0, n\uc740 \ud56d\uc0c1 \uc9dd\uc218\uc774\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574 \ubb38\uc81c\uc758 \uc870\uac74\uc744 \uc9c0\ud0a4\uba70 \uc790\ub9ac\ub97c \ubc14\uafc0 \uc218 \uc788\ub294 \ubc29\ubc95\uc758 \uc218\ub97c \ucd9c\ub825\ud558\ub77c.&nbsp;\ub2e8, \ubb38\uc81c\uc758 \ub2f5\uc774 \ub9e4\uc6b0 \ucee4\uc9c8 \uc218 \uc788\uc73c\ubbc0\ub85c \ub9c8\uc9c0\ub9c9 \uc5ec\uc12f\uc790\ub9ac\ub9cc \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"9278","problem_lang":"1","title":"Frustrated Queue","description":"<p>The toilet in Freddy&rsquo;s garden is broken, so his only chance are public toilets nearby. One day, there is a long queue of people in front of the toilets. Freddy is in a big need and so he desperately wants the queue to be served as quick as possible.<\/p>\r\n\r\n<p>To use the toilets, you need to pay 5 crowns. Half of the people in the queue have a 5-crown coin and the other half only have a 10-crown coin. Initially, the toilet operator has no coins, thus, the people in the queue have to reorganize so that whenever someone wants to pay with a 10-crown coin, the operator has at least one 5-crown coin available from previous customers.<\/p>\r\n\r\n<p>The issue is that some of the people in the queue are unwilling to give up their spot. Determine in how many ways can the people willing to change their position rearrange themselves in the queue so that the operator always has change available. The positions of those unwilling cannot change (they cannot be moved to a later but also to an earlier spot in the rearranged queue). Furthermore, among those willing to change the position, the relative order of those with the same coin must be preserved.<\/p>\r\n","input":"<p>The input contains several test cases. Each test case consists of one line containing a non-empty string of parentheses and dots of length n &le; 1 000. A dot indicates a person willing to change their position in the queue, an opening parenthesis indicates a person unwilling to change the position who has a 5-crown coin, and a closing parenthesis indicates a person unwilling to change the position who has a 10-crown coin.<\/p>\r\n\r\n<p>You may assume that n is even and that the string contains at most n\/2 opening parentheses and at most n\/2 closing ones.<\/p>\r\n","output":"<p>For each test case, compute the number of ways the queue can be rearranged so that the conditions described in the statement of the problem are satis\ufb01ed. Since this number may be too large, you are only required to print a single line containing one integer equal to the last 6 digits (in the decimal representation) of the number.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]