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문제

알파벳 소문자들로만 이루어진 문자열을 생각하자. 이런 문자열을 읽어 나가다 보면, 문자열의 주기가 예측되는 순간이 있다. 다음과 같은 문자열을 예로 들어 보자.

a b a b a b a

이 문자열을 네 번째 문자까지의 문자열 'a b a b'와, 그 뒤에 남은 'a b a'로 나누어 생각해 볼 수 있다. 이렇게 하면 뒤쪽 문자열은 앞쪽 네 개의 문자 중 세 번째 문자까지가 반복되다가 끝나는 꼴이다.

a b a b a b a

또한, 여섯 번째 문자까지의 문자열 'a b a b a b'와, 그 뒤에 남은 'a'로 나누어서 생각할 수도 있다. 이 경우에도 뒤쪽 문자열은 앞쪽 문자열이 반복되다가 끝나는 꼴이다.

즉, 예시된 문자열은 'a b a b'혹은, 'a b a b a b'가 반복되는 문자열의 일부라고 예상할 수 있는 것이다. 단, 이러한 추정에서 뒤쪽 문자열이 앞쪽 문자열보다 길면 안 된다. 예를 들어 'a b'는 이 문자열의 주기로 예측하기에는 너무 짧다.

이제는 어떤 문자열 S에 대해, 첫 번째 문자부터, i번째 문자까지로 이루어진 부분 문자열 Si를 생각해 보자. 모든  각각에 대해, 위에 예시된 것처럼 문자열의 주기를 추정할 수 있다. 우리가 관심 있는 것은 이렇게  각각에 Si에 대해 추정할 수 있는 주기 중 가장 긴 것의 길이이다. 이를 Pi라고 하자. 예시된 문자열에서 P7은 4와 6중 최댓값인 6이 된다.

길이가 n인 문자열 S가 주어졌을 때, P1 + P2 + ... + Pn을 구하는 프로그램을 작성하시오.

입력

첫째 줄에 문자열 S의 길이 n이 주어진다. (1 ≤ n ≤ 1,000,000) 둘째 줄에 문자열 S가 공백 없이 주어진다.

출력

첫째 줄에, P1 + P2 + ... + Pn의 값을 출력한다.

예제 입력 1

8
babababa

예제 출력 1

24

힌트

P8 = 6, P7 = 6, P6 = 4, P5 = 4, P4 = 2, P3 = 2, P2 = 0, P1 = 0

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(1 &le; n &le; 1,000,000) \ub458\uc9f8 \uc904\uc5d0 \ubb38\uc790\uc5f4 S\uac00 \uacf5\ubc31 \uc5c6\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0, P<sub>1<\/sub> + P<sub>2<\/sub> + ... + P<sub>n<\/sub>\uc758 \uac12\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>P<sub>8<\/sub> = 6, P<sub>7<\/sub> = 6, P<sub>6<\/sub> = 4, P<sub>5<\/sub> = 4, P<sub>4<\/sub> = 2, P<sub>3<\/sub> = 2, P<sub>2<\/sub> = 0, P<sub>1<\/sub> = 0<\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"1787","problem_lang":"1","title":"Periods of Words","description":"<p>A string is a finite sequence of lower-case (non-capital) letters of the English alphabet. Particularly, it may be an empty sequence, i.e. a sequence of 0 letters. By A = BC we denotes that A is a string obtained by concatenation (joining by writing one immediately after another, i.e. without any space, etc.) of the strings B and C (in this order). A string P is a prefix of the string A, if there is a string B, that A = PB. In other words, prefixes of A are the initial fragments of A. In addition, if P &ne; A and P is not an empty string, we say, that P is a proper prefix of A.<\/p>\r\n\r\n<p>A string Q is a period of A, If Q is proper prefix of A and A is a prefix (not necessarily a proper one) of the string QQ. For example, the strings <code>abab<\/code> and <code>ababab<\/code> are both periods of the string <code>abababa<\/code>. The maximum period of a string A is the longest of its periods or the empty string, If A doesn&#39;t have any period. For example, the maximum period of <code>ababab<\/code> is <code>abab<\/code>. 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출처

Olympiad > Polish Olympiad in Informatics > POI 2005/2006 > Stage 1 2번