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문제

KSAAC 운영진은 모두 KSA를 사랑하기 때문에 다음 조건을 만족하는 문자열을 좋아한다.

문자열의 길이를 $N$이라고 할 때, $1 \leq i \leq N$인 모든 $i$에 대하여

  • $i$를 $3$으로 나눈 나머지가 $1$이면 $i$번째 문자는 K이다.
  • $i$를 $3$으로 나눈 나머지가 $2$이면 $i$번째 문자는 S이다.
  • $i$를 $3$으로 나눈 나머지가 $0$이면 $i$번째 문자는 A이다.

문자열에는 다음 시행을 $0$회 이상 할 수 있으며 매회 둘 중 하나를 선택하여 시행할 수 있다.

  • 존재하는 문자들 중 인접한 문자 2개를 제거한다.
  • 문자열의 맨 앞에 동일한 문자를 2개 추가한다.

주어진 문자열 $X$에 적절한 시행을 하여 $X$를 $X$와 길이가 같으면서 KSAAC 운영진이 좋아하는 문자열로 바꾸려고 한다. 이때 필요한 시행의 최소 횟수를 구하여라.

입력

첫 번째 줄에 문자열 $X$가 주어진다.

출력

문자열 $X$를 $X$와 길이가 같으면서 KSAAC 운영진이 좋아하는 문자열로 바꾸기 위한 최소 시행 횟수를 출력한다.

주어진 시행을 유한 번 하는 것으로 문자열 $X$를 $X$와 길이가 같으면서 KSAAC 운영진이 좋아하는 문자열로 바꿀 수 있음이 보장된다.

제한

  • $1 \le |X| \le 5 \times 10^5$
  • $X_i \in \{$ K$,$ S$,$ A$\}$

서브태스크

번호배점제한
120

$X$의 모든 문자가 동일

280

추가 제약 조건 없음

예제 입력 1

KSKA

예제 출력 1

8

주어진 문자열을 KSAK로 만드는 것이 목표이다.

KK, SS, AA, KK를 추가하면 문자열이 KKSSAAKKKSKA가 되는데 여기서 $2$, $6$, $9$, $11$번째 문자와 그 오른쪽에 위치한 문자를 삭제하면 KSAK가 된다.

예제 입력 2

KKK

예제 출력 2

6

주어진 문자열을 KSA로 만드는 것이 목표이다.

KK, SS, AA를 추가하면 문자열이 KKSSAAKKK가 되는데 여기서 $2$, $6$, $8$번째 문자와 그 오른쪽에 위치한 문자를 삭제하면 KSA가 된다.

[{"problem_id":"35297","problem_lang":"0","title":"KSA \ubb38\uc790\uc5f4 3","description":"<p>KSAAC \uc6b4\uc601\uc9c4\uc740 \ubaa8\ub450 KSA\ub97c \uc0ac\ub791\ud558\uae30 \ub54c\ubb38\uc5d0 \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\ud558\ub294 \ubb38\uc790\uc5f4\uc744 \uc88b\uc544\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ubb38\uc790\uc5f4\uc758 \uae38\uc774\ub97c $N$\uc774\ub77c\uace0 \ud560 \ub54c, $1 \\leq i \\leq N$\uc778 \ubaa8\ub4e0 $i$\uc5d0 \ub300\ud558\uc5ec<\/p>\r\n\r\n<ul>\r\n<li>$i$\ub97c $3$\uc73c\ub85c \ub098\ub208 \ub098\uba38\uc9c0\uac00 $1$\uc774\uba74 $i$\ubc88\uc9f8 \ubb38\uc790\ub294 <span style=\"color:#e74c3c;\"><code>K<\/code><\/span>\uc774\ub2e4.<\/li>\r\n<li>$i$\ub97c $3$\uc73c\ub85c \ub098\ub208 \ub098\uba38\uc9c0\uac00 $2$\uc774\uba74 $i$\ubc88\uc9f8 \ubb38\uc790\ub294 <span style=\"color:#e74c3c;\"><code>S<\/code><\/span>\uc774\ub2e4.<\/li>\r\n<li>$i$\ub97c $3$\uc73c\ub85c \ub098\ub208 \ub098\uba38\uc9c0\uac00 $0$\uc774\uba74 $i$\ubc88\uc9f8 \ubb38\uc790\ub294 <span style=\"color:#e74c3c;\"><code>A<\/code><\/span>\uc774\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\ubb38\uc790\uc5f4\uc5d0\ub294 \ub2e4\uc74c \uc2dc\ud589\uc744 $0$\ud68c \uc774\uc0c1 \ud560 \uc218 \uc788\uc73c\uba70 \ub9e4\ud68c \ub458 \uc911 \ud558\ub098\ub97c \uc120\ud0dd\ud558\uc5ec \uc2dc\ud589\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<ul>\r\n<li>\uc874\uc7ac\ud558\ub294 \ubb38\uc790\ub4e4 \uc911 \uc778\uc811\ud55c \ubb38\uc790 2\uac1c\ub97c \uc81c\uac70\ud55c\ub2e4.<\/li>\r\n<li>\ubb38\uc790\uc5f4\uc758 \ub9e8 \uc55e\uc5d0 \ub3d9\uc77c\ud55c \ubb38\uc790\ub97c 2\uac1c \ucd94\uac00\ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc8fc\uc5b4\uc9c4 \ubb38\uc790\uc5f4 $X$\uc5d0 \uc801\uc808\ud55c \uc2dc\ud589\uc744 \ud558\uc5ec $X$\ub97c $X$\uc640 \uae38\uc774\uac00 \uac19\uc73c\uba74\uc11c KSAAC \uc6b4\uc601\uc9c4\uc774 \uc88b\uc544\ud558\ub294 \ubb38\uc790\uc5f4\ub85c \ubc14\uafb8\ub824\uace0 \ud55c\ub2e4. \uc774\ub54c \ud544\uc694\ud55c \uc2dc\ud589\uc758 \ucd5c\uc18c \ud69f\uc218\ub97c \uad6c\ud558\uc5ec\ub77c.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \ubb38\uc790\uc5f4 $X$\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\ubb38\uc790\uc5f4 $X$\ub97c $X$\uc640 \uae38\uc774\uac00 \uac19\uc73c\uba74\uc11c KSAAC \uc6b4\uc601\uc9c4\uc774 \uc88b\uc544\ud558\ub294 \ubb38\uc790\uc5f4\ub85c \ubc14\uafb8\uae30 \uc704\ud55c \ucd5c\uc18c \uc2dc\ud589 \ud69f\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc8fc\uc5b4\uc9c4 \uc2dc\ud589\uc744 \uc720\ud55c \ubc88 \ud558\ub294 \uac83\uc73c\ub85c \ubb38\uc790\uc5f4 $X$\ub97c $X$\uc640 \uae38\uc774\uac00 \uac19\uc73c\uba74\uc11c KSAAC \uc6b4\uc601\uc9c4\uc774 \uc88b\uc544\ud558\ub294 \ubb38\uc790\uc5f4\ub85c \ubc14\uafc0 \uc218 \uc788\uc74c\uc774 \ubcf4\uc7a5\ub41c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n<li>$1 \\le |X| \\le 5 \\times 10^5$<\/li>\r\n<li>$X_i \\in \\{$ <span style=\"color:#e74c3c;\"><code>K<\/code><\/span>$,$ <span style=\"color:#e74c3c;\"><code>S<\/code><\/span>$,$ <span style=\"color:#e74c3c;\"><code>A<\/code><\/span>$\\}$<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$X$\uc758 \ubaa8\ub4e0 \ubb38\uc790\uac00 \ub3d9\uc77c<\/p>\r\n","subtask2":"<p>\ucd94\uac00 \uc81c\uc57d \uc870\uac74 \uc5c6\uc74c<\/p>\r\n","sample_explain_1":"<p>\uc8fc\uc5b4\uc9c4 \ubb38\uc790\uc5f4\uc744 <span style=\"color:#e74c3c;\"><code>KSAK<\/code><\/span>\ub85c \ub9cc\ub4dc\ub294 \uac83\uc774 \ubaa9\ud45c\uc774\ub2e4. <\/p>\r\n\r\n<p><span style=\"color:#e74c3c;\"><code>KK<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>SS<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>AA<\/code><\/span>, <code><span style=\"color:#e74c3c;\">KK<\/span><\/code>\ub97c \ucd94\uac00\ud558\uba74 \ubb38\uc790\uc5f4\uc774 <code><span style=\"color:#e74c3c;\">KKSSAAKKKSKA<\/span><\/code>\uac00 \ub418\ub294\ub370 \uc5ec\uae30\uc11c $2$, $6$, $9$, $11$\ubc88\uc9f8 \ubb38\uc790\uc640 \uadf8 \uc624\ub978\ucabd\uc5d0 \uc704\uce58\ud55c \ubb38\uc790\ub97c \uc0ad\uc81c\ud558\uba74 <span style=\"color:#e74c3c;\"><code>KSAK<\/code><\/span>\uac00 \ub41c\ub2e4. <\/p>\r\n","sample_explain_2":"<p>\uc8fc\uc5b4\uc9c4 \ubb38\uc790\uc5f4\uc744 <span style=\"color:#e74c3c;\"><code>KSA<\/code><\/span>\ub85c \ub9cc\ub4dc\ub294 \uac83\uc774 \ubaa9\ud45c\uc774\ub2e4. <\/p>\r\n\r\n<p><span style=\"color:#e74c3c;\"><code>KK<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>SS<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>AA<\/code><\/span>\ub97c \ucd94\uac00\ud558\uba74 \ubb38\uc790\uc5f4\uc774 <code><span style=\"color:#e74c3c;\">KKSSAAKKK<\/span><\/code>\uac00 \ub418\ub294\ub370 \uc5ec\uae30\uc11c $2$, $6$, $8$\ubc88\uc9f8 \ubb38\uc790\uc640 \uadf8 \uc624\ub978\ucabd\uc5d0 \uc704\uce58\ud55c \ubb38\uc790\ub97c \uc0ad\uc81c\ud558\uba74 <span style=\"color:#e74c3c;\"><code>KSA<\/code><\/span>\uac00 \ub41c\ub2e4.<\/p>\r\n"},{"problem_id":"35297","problem_lang":"1","title":"KSA String 3","description":"<p>Because the KSAAC staff love KSA, they like strings that satisfy the following conditions.<\/p>\r\n\r\n<p>When the length of the string is $N$, for all $i$ such that $1 \\leq i \\leq N$<\/p>\r\n\r\n<ul>\r\n\t<li>If the remainder after dividing $i$ by $3$ is $1$, the $i$th character is <span style=\"color:#e74c3c;\"><code>K<\/code><\/span>.<\/li>\r\n\t<li>If the remainder after dividing $i$ by $3$ is $2$, the $i$th character is <span style=\"color:#e74c3c;\"><code>S<\/code><\/span>.<\/li>\r\n\t<li>If the remainder after dividing $i$ by $3$ is $0$, the $i$th character is <span style=\"color:#e74c3c;\"><code>A<\/code><\/span>.<\/li>\r\n<\/ul>\r\n\r\n<p>The following operations can be performed $0$ or more times on the string, selecting one of the two each time.<\/p>\r\n\r\n<ul>\r\n\t<li>Remove two adjacent characters from the string.<\/li>\r\n\t<li>Add two identical characters to the beginning of the string.<\/li>\r\n<\/ul>\r\n\r\n<p>By performing appropriate operations on the given string $X$, we want to change $X$ into a string that the KSAAC staff like with the same length as $X$. Find the minimum number of operations required.<\/p>\r\n","input":"<p>The first line contains a string $X$.<\/p>\r\n","output":"<p>Print the minimum number of operations needed to change the given string $X$ into a string that the KSAAC staff like with the same length as $X$.<\/p>\r\n\r\n<p>It is guaranteed that by performing the given operations a finite number of times, the given string $X$ can be changed into a string that the KSAAC staff like with the same length as $X$.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>$1 \\le |X| \\le 5 \\times 10^5$<\/li>\r\n\t<li>$X_i \\in \\{$ <span style=\"color:#e74c3c;\"><code>K<\/code><\/span>$,$ <span style=\"color:#e74c3c;\"><code>S<\/code><\/span>$,$ <span style=\"color:#e74c3c;\"><code>A<\/code><\/span>$\\}$<\/li>\r\n<\/ul>\r\n","subtask1":"<p>All characters in string $X$ are identical<\/p>\r\n","subtask2":"<p>No additional constraints<\/p>\r\n","sample_explain_1":"<p>The goal is to change the given string to <span style=\"color:#e74c3c;\"><code>KSAK<\/code><\/span>.<\/p>\r\n\r\n<p>Adding <span style=\"color:#e74c3c;\"><code>KK<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>SS<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>AA<\/code><\/span>, <code><span style=\"color:#e74c3c;\">KK<\/span><\/code> makes the string <code><span style=\"color:#e74c3c;\">KKSSAAKKKSKA<\/span><\/code>. Deleting the second, sixth, ninth, and eleventh characters, along with the characters to their right, yields the KSA string.<\/p>\r\n","sample_explain_2":"<p>The goal is to change the given string to <span style=\"color:#e74c3c;\"><code>KSA<\/code><\/span>.<\/p>\r\n\r\n<p>Adding <span style=\"color:#e74c3c;\"><code>KK<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>SS<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>AA<\/code><\/span> makes the string <code><span style=\"color:#e74c3c;\">KKSSAAKKK<\/span><\/code>. Deleting the second, sixth, and eighth characters, along with the characters to their right, yields the KSA string.<\/p>\r\n"}]

채점 및 기타 정보

  • 예제는 채점하지 않는다.
  • 이 문제의 채점 우선 순위는 2이다.