시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 128 MB 50 26 22 47.826%

문제

몇 개의 정점으로 이루어진 트리가 있다. 이 트리는 루트가 있는 트리이며, 각 정점은 몇 개의 자식 정점을 가질 수 있다. 각각의 정점에는 알파벳 대문자가 적혀 있다. 같은 문자가 여러 정점에 적혀 있을 수도 있다.

이 트리를 루트부터 시작해서 탐색하는데, 어떤 한 정점에서는 그 정점의 자식들 중 왼쪽 자식들부터 차례대로 방문해 나간다. 이와 같이 탐색하면 하나의 경로를 얻을 수 있다. 주의할 점은, 자식이 있는 정점의 경우에는 여러 번 방문될 수도 있는데(제일 처음 방문할 때와, 자식 정점을 방문하고 다시 돌아올 때), 그러한 경우에 한 정점이 여러 번 경로에 나타날 수도 있다는 것이다.

위의 그림은 경로가 ABABABA인 경우를 모두 나타낸 것이다. 아래쪽이 루트를 의미하며, 위로 연결된 것이 자식 노드를 의미한다. 위의 그림에서는 왼쪽 자식을 왼쪽에 나타냈는데, 대부분의 사람이 생각하는 그림처럼 루트가 위에 있는 그림으로 고치려면, 좌우 대칭을 해야 한다. 물론 답에는 변화가 없다.

경로가 주어졌을 때, 그러한 경로를 갖는 트리의 개수를 구해내는 프로그램을 작성하시오.

입력

첫째 줄에 경로가 주어진다. 이는 알파벳 대문자로만 이루어지며, 그 길이가 300자를 넘지 않는다.

출력

첫째 줄에 트리의 개수를 1,000,000,000으로 나눈 나머지를 출력한다.

예제 입력 1

ABABABA

예제 출력 1

5

힌트

[{"problem_id":"2088","problem_lang":"0","title":"\ud2b8\ub9ac\uc758 \uac1c\uc218","description":"<p>\uba87 \uac1c\uc758 \uc815\uc810\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \ud2b8\ub9ac\uac00 \uc788\ub2e4. \uc774 \ud2b8\ub9ac\ub294 \ub8e8\ud2b8\uac00 \uc788\ub294 \ud2b8\ub9ac\uc774\uba70, \uac01 \uc815\uc810\uc740 \uba87 \uac1c\uc758 \uc790\uc2dd \uc815\uc810\uc744 \uac00\uc9c8 \uc218 \uc788\ub2e4. \uac01\uac01\uc758 \uc815\uc810\uc5d0\ub294 \uc54c\ud30c\ubcb3 \ub300\ubb38\uc790\uac00 \uc801\ud600 \uc788\ub2e4. \uac19\uc740 \ubb38\uc790\uac00 \uc5ec\ub7ec \uc815\uc810\uc5d0 \uc801\ud600 \uc788\uc744 \uc218\ub3c4 \uc788\ub2e4.<\/p>\r\n<p>\uc774 \ud2b8\ub9ac\ub97c \ub8e8\ud2b8\ubd80\ud130 \uc2dc\uc791\ud574\uc11c \ud0d0\uc0c9\ud558\ub294\ub370, \uc5b4\ub5a4 \ud55c \uc815\uc810\uc5d0\uc11c\ub294 \uadf8 \uc815\uc810\uc758 \uc790\uc2dd\ub4e4 \uc911 \uc67c\ucabd \uc790\uc2dd\ub4e4\ubd80\ud130 \ucc28\ub840\ub300\ub85c \ubc29\ubb38\ud574 \ub098\uac04\ub2e4. \uc774\uc640 \uac19\uc774 \ud0d0\uc0c9\ud558\uba74 \ud558\ub098\uc758 \uacbd\ub85c\ub97c \uc5bb\uc744 \uc218 \uc788\ub2e4. \uc8fc\uc758\ud560 \uc810\uc740, \uc790\uc2dd\uc774 \uc788\ub294 \uc815\uc810\uc758 \uacbd\uc6b0\uc5d0\ub294 \uc5ec\ub7ec \ubc88 \ubc29\ubb38\ub420 \uc218\ub3c4 \uc788\ub294\ub370(\uc81c\uc77c \ucc98\uc74c \ubc29\ubb38\ud560 \ub54c\uc640, \uc790\uc2dd \uc815\uc810\uc744 \ubc29\ubb38\ud558\uace0 \ub2e4\uc2dc \ub3cc\uc544\uc62c \ub54c), \uadf8\ub7ec\ud55c \uacbd\uc6b0\uc5d0 \ud55c \uc815\uc810\uc774 \uc5ec\ub7ec \ubc88 \uacbd\ub85c\uc5d0 \ub098\ud0c0\ub0a0 \uc218\ub3c4 \uc788\ub2e4\ub294 \uac83\uc774\ub2e4.<\/p>\r\n<p><img width=\"567\" height=\"175\" alt=\"\" src=\"\/JudgeOnline\/upload\/201007\/trtrtrtr.png\" \/><\/p>\r\n<p>\uc704\uc758 \uadf8\ub9bc\uc740 \uacbd\ub85c\uac00 ABABABA\uc778 \uacbd\uc6b0\ub97c \ubaa8\ub450 \ub098\ud0c0\ub0b8 \uac83\uc774\ub2e4. \uc544\ub798\ucabd\uc774 \ub8e8\ud2b8\ub97c \uc758\ubbf8\ud558\uba70, \uc704\ub85c \uc5f0\uacb0\ub41c \uac83\uc774 \uc790\uc2dd \ub178\ub4dc\ub97c \uc758\ubbf8\ud55c\ub2e4. \uc704\uc758 \uadf8\ub9bc\uc5d0\uc11c\ub294 \uc67c\ucabd \uc790\uc2dd\uc744 \uc67c\ucabd\uc5d0 \ub098\ud0c0\ub0c8\ub294\ub370, \ub300\ubd80\ubd84\uc758 \uc0ac\ub78c\uc774 \uc0dd\uac01\ud558\ub294 \uadf8\ub9bc\ucc98\ub7fc \ub8e8\ud2b8\uac00 \uc704\uc5d0 \uc788\ub294 \uadf8\ub9bc\uc73c\ub85c \uace0\uce58\ub824\uba74, \uc88c\uc6b0 \ub300\uce6d\uc744 \ud574\uc57c \ud55c\ub2e4. \ubb3c\ub860 \ub2f5\uc5d0\ub294 \ubcc0\ud654\uac00 \uc5c6\ub2e4.<\/p>\r\n<p>\uacbd\ub85c\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uadf8\ub7ec\ud55c \uacbd\ub85c\ub97c \uac16\ub294 \ud2b8\ub9ac\uc758 \uac1c\uc218\ub97c \uad6c\ud574\ub0b4\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \uacbd\ub85c\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ub294 \uc54c\ud30c\ubcb3 \ub300\ubb38\uc790\ub85c\ub9cc \uc774\ub8e8\uc5b4\uc9c0\uba70, \uadf8 \uae38\uc774\uac00 300\uc790\ub97c \ub118\uc9c0 \uc54a\ub294\ub2e4.<\/p>","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud2b8\ub9ac\uc758 \uac1c\uc218\ub97c 1,000,000,000\uc73c\ub85c \ub098\ub208 \ub098\uba38\uc9c0\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2088","problem_lang":"1","title":"Exploring Pyramids","description":"<p>Archaeologists have discovered a new set of hidden caves in one of the Egyptian pyramids. The decryption of ancient hieroglyphs on the walls nearby showed that the caves structure is as follows. There are n caves in a pyramid, connected by narrow passages, one of the caves is connected by a passage to the outer world. The system of the passages is organized in such a way, that there is exactly one way to get from outside to each cave along passages. All caves are located in the basement of the pyramid, so we can consider them being located in the same plane. Passages do not intersect. Each cave has its walls colored in one of several various colors.<\/p>\r\n\r\n<p>The scientists have decided to create a more detailed description of the caves, so they decided to use an exploring robot. The robot they are planning to use has two types of memory &mdash; the output tape, which is used for writing down the description of the caves, and the operating memory organized as a stack.<\/p>\r\n\r\n<p>The robot first enters the cave connected to the outer world along the passage. When it travels along any passage for the first time, it puts its description on the top of its stack. When the robot enters any cave, it prints the color of its walls to its output tape. After that it chooses the leftmost passage among those that it has not yet travelled and goes along it. If there is no such passage, the robot takes the passage description from the top of its stack and travels along it in the reverse direction. The robot&rsquo;s task is over when it returns to the outside of the pyramid. It is easy to see that during its trip the robot visits each cave at least once and travels along each passage exactly once in each direction.<\/p>\r\n\r\n<p>The scientists have sent the robot to its mission. After it returned they started to study the output tape. What a great disappointment they have had after they have understood that the output tape does not describe the cave system uniquely. Now they have a new problem &mdash; they want to know how many di\ufb00erent cave systems could have produced the output tape they have. Help them to find that out.<\/p>\r\n\r\n<p>Since the requested number can be quite large, you should output it modulo 1 000 000 000. Please note, that the absolute locations of the caves are not important, but their relative locations are important, so the caves (c) and (d) on the picture below are considered di\ufb00erent.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/pyramid.png\" style=\"height:155px; width:654px\" \/><\/p>\r\n","input":"<p>The input file contains the output tape that the archaeologists have. The output tape is the sequence of colors of caves in order the robot visited them. The colors are denoted by capital letters of the English alphabet. The length of the tape does not exceed 300 characters.<\/p>\r\n","output":"<p>Output one integer number &mdash; the number of different cave systems (modulo 1 000 000 000) that could produce the output tape.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]