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문제

이 문제는 인터랙티브 문제이다.

숨겨진 수열 $S$가 있다. 당신은 이 수열 $S$에 관한 정보를 알아내야 한다. 수열 $S$의 길이는 $N$이고, 아래의 조건에 모두 맞는다.

  • $S$의 모든 원소는 $1$, $2$, $3$, $4$ 중 하나이다.
  • $S_1=1$이다.
  • $S_i=1$이라면, $S_{i+1}=1$ 또는 $S_{i+1}=2$이다. $(1\le i<N)$
  • $S_i=2$이라면, $S_{i+1}=2$ 또는 $S_{i+1}=3$이다. $(1\le i<N)$
  • $S_i=3$이라면, $S_{i+1}=3$ 또는 $S_{i+1}=4$이다. $(1\le i<N)$
  • $S_i=4$이라면, $S_{i+1}=4$ 또는 $S_{i+1}=1$이다. $(1\le i<N)$

당신은 다음과 같은 두 가지 질문을 할 수 있다.

  • count l r: $[l,r]$ 구간 내에 있는 $1$, $2$, $3$, $4$의 개수를 오름차순으로 정렬한 수열을 질문한다.
  • diff l r: $l\le i<r$이고 $S_i\neq S_{i+1}$인 $i$의 개수를 질문한다.

이때, $S$에 $1$, $2$, $3$, $4$가 각각 몇 개씩 있는지 알아내어라.

인터랙션

첫 줄에는 테스트 케이스의 수 $T$가 주어진다.

각 테스트 케이스의 시작에 수열 $S$의 길이를 나타내는 정수 $N$이 입력으로 주어진다.

질문을 하기 위해서는 다음 중 하나의 형식으로 출력한 뒤 버퍼를 비워야 한다.

  • count l r
  • diff l r

만약 질문이 count라면, 입력으로 네 정수를 입력받아야 한다. 이 네 개의 정수는 구간 $[l,r]$에서 $1$, $2$, $3$, $4$의 개수를 오름차순으로 정렬한 배열이다.

만약 질문이 diff라면, 입력으로 하나의 정수를 입력받아야 한다. 이 정수는 $l\le i<r$이고 $S_i\neq S_{i+1}$인 $i$의 개수를 나타낸다.

답을 알았다면, 다음과 같은 형식으로 출력한 뒤 버퍼를 비워야 한다. 이때, c1, c2, c3, c4는 각각 수열 $S$에서 $1$, $2$, $3$, $4$의 개수와 일치해야 한다.

  • answer c1 c2 c3 c4

당신의 프로그램이 조건에 맞지 않는 질문을 하거나, 질문 횟수를 초과하거나, 직전의 테스트 케이스에 대해 제시한 답이 틀린 경우 질문에 대한 답, 또는 $N$의 값 대신 $-1$을 입력받게 된다. 이 경우에 당신의 프로그램은 즉시 종료해야 하고, 채점 결과는 '틀렸습니다'를 받게 된다. 만약 프로그램이 곧바로 종료하지 않는다면 예상치 못한 채점 결과를 받을 수 있다.

하나의 테스트 케이스를 해결한 뒤에도 당신의 프로그램은 곧바로 다음 테스트 케이스로 진행해야 한다. 모든 테스트 케이스를 해결한 뒤 프로그램은 즉시 종료되어야 한다.

제한

  • $1\leq T\leq 100$
  • $1\leq N\leq 1\ 000$
  • $S_1=1$
  • $1\leq S_i\leq 4$ $(2\leq i\leq N)$
  • $S_i=1\implies S_{i+1}\in\{1,2\}$ $(1\leq i<N)$
  • $S_i=2\implies S_{i+1}\in\{2,3\}$ $(1\leq i<N)$
  • $S_i=3\implies S_{i+1}\in\{3,4\}$ $(1\leq i<N)$
  • $S_i=4\implies S_{i+1}\in\{4,1\}$ $(1\leq i<N)$
  • 모든 질문에서 $1\leq l\leq r\leq N$이어야 한다.
  • 인터랙터는 비적응적이다. 수열 $S$는 사전에 결정되어 있고, 질문에 따라 변하지 않는다.

점수

이 문제의 점수는 각 테스트 케이스의 질문 횟수 중 최댓값 $Q_{max}$에 따라 결정된다. $\lfloor x\rfloor$은 $x$ 이하의 최대 정수이다.

  • $1000<Q_{max}$ : $0$점
  • $100<Q_{max}\leq 1000$ : $10$점
  • $50<Q_{max}\leq 100$ : $\lfloor 50-0.4Q_{max}\rfloor$점
  • $30<Q_{max}\leq 50$ : $80-Q_{max}$점
  • $19<Q_{max}\leq 30$ : $\lfloor 98-1.6Q_{max}\rfloor$점
  • $Q_{max}=19$ : $70$점
  • $Q_{max}=18$ : $75$점
  • $Q_{max}=17$ : $82$점
  • $Q_{max}=16$ : $90$점
  • $Q_{max}\leq 15$ : $100$점

예제 입력 1

1
2

0

0 0 0 2

예제 출력 1



diff 1 2

count 1 2

answer 2 0 0 0

위 예제의 테스트 케이스는 하나이고, 정답 수열은 $S=[1,1]$이다.

당신의 프로그램은 먼저 수열의 길이 $N$을 입력받는다. 이 테스트 케이스에서 수열 $S$의 길이는 $2$이다.

당신의 프로그램은 diff 1 2를 출력해 질문한다. $1\le i<2$이고 $S_i\neq S_{i+1}$인 $i$가 없으므로, 답으로 정수 $0$이 주어진다.

당신의 프로그램은 count 1 2를 출력해 질문한다. 수열의 구간 $[1,2]$에서 $1$, $2$, $3$, $4$의 개수는 각각 $2$개, $0$개, $0$개, $0$개이므로, 답으로 네 정수 $0$, $0$, $0$, $2$가 주어진다.

당신의 프로그램은 answer 2 0 0 0을 출력한다. 이것은 $1$, $2$, $3$, $4$의 개수가 각각 $2$개, $0$개, $0$개, $0$개라는 뜻이다. 정답을 맞혔으므로 해당 테스트 케이스가 종료된다.

주어진 예시는 입출력이 어떤 방식으로 이루어지는지 이해를 돕기 위해 의도적으로 개행 간격 등을 조절한 것이며, 실제 입출력에서는 빈 줄을 출력하지 말아야 한다.

노트

출력 버퍼를 비우는 방법은 다음과 같다.

  • C: fflush(stdout)
  • C++: std::cout << std::flush
  • Java: System.out.flush()
  • Python: sys.stdout.flush()

이외의 언어에 대해서는 언어별 명세를 참고해야 한다.

[{"problem_id":"31074","problem_lang":"0","title":"\uc2f1\uae00 \ud50c\ub808\uc774\uc5b4 \uac8c\uc784","description":"<p>\uc774 \ubb38\uc81c\ub294 <strong>\uc778\ud130\ub799\ud2f0\ube0c \ubb38\uc81c<\/strong>\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc228\uaca8\uc9c4 \uc218\uc5f4 $S$\uac00 \uc788\ub2e4. \ub2f9\uc2e0\uc740 \uc774 \uc218\uc5f4 $S$\uc5d0 \uad00\ud55c \uc815\ubcf4\ub97c \uc54c\uc544\ub0b4\uc57c \ud55c\ub2e4. \uc218\uc5f4 $S$\uc758 \uae38\uc774\ub294 $N$\uc774\uace0, \uc544\ub798\uc758 \uc870\uac74\uc5d0 \ubaa8\ub450 \ub9de\ub294\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>$S$\uc758 \ubaa8\ub4e0 \uc6d0\uc18c\ub294 $1$, $2$, $3$, $4$ \uc911 \ud558\ub098\uc774\ub2e4.<\/li>\r\n\t<li>$S_1=1$\uc774\ub2e4.<\/li>\r\n\t<li>$S_i=1$\uc774\ub77c\uba74, $S_{i+1}=1$ \ub610\ub294 $S_{i+1}=2$\uc774\ub2e4. $(1\\le i&lt;N)$<\/li>\r\n\t<li>$S_i=2$\uc774\ub77c\uba74, $S_{i+1}=2$ \ub610\ub294 $S_{i+1}=3$\uc774\ub2e4. $(1\\le i&lt;N)$<\/li>\r\n\t<li>$S_i=3$\uc774\ub77c\uba74, $S_{i+1}=3$ \ub610\ub294 $S_{i+1}=4$\uc774\ub2e4. $(1\\le i&lt;N)$<\/li>\r\n\t<li>$S_i=4$\uc774\ub77c\uba74, $S_{i+1}=4$ \ub610\ub294 $S_{i+1}=1$\uc774\ub2e4. $(1\\le i&lt;N)$<\/li>\r\n<\/ul>\r\n\r\n<p>\ub2f9\uc2e0\uc740 \ub2e4\uc74c\uacfc \uac19\uc740 \ub450 \uac00\uc9c0 \uc9c8\ubb38\uc744 \ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li><span style=\"color:#e74c3c;\"><code>count l r<\/code><\/span>: $[l,r]$ \uad6c\uac04 \ub0b4\uc5d0 \uc788\ub294 $1$, $2$, $3$, $4$\uc758 \uac1c\uc218\ub97c <strong>\uc624\ub984\ucc28\uc21c<\/strong>\uc73c\ub85c \uc815\ub82c\ud55c \uc218\uc5f4\uc744 \uc9c8\ubb38\ud55c\ub2e4.<\/li>\r\n\t<li><span style=\"color:#e74c3c;\"><code>diff l r<\/code><\/span>: $l\\le i&lt;r$\uc774\uace0 $S_i\\neq S_{i+1}$\uc778 $i$\uc758 \uac1c\uc218\ub97c \uc9c8\ubb38\ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc774\ub54c, $S$\uc5d0 $1$, $2$, $3$, $4$\uac00 <strong>\uac01\uac01 \uba87 \uac1c\uc529 \uc788\ub294\uc9c0<\/strong> \uc54c\uc544\ub0b4\uc5b4\ub77c.<\/p>\r\n","input":"","output":"","hint":"<p>\ucd9c\ub825 \ubc84\ud37c\ub97c \ube44\uc6b0\ub294 \ubc29\ubc95\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>C: <span style=\"color:#e74c3c;\"><code>fflush(stdout)<\/code><\/span><\/li>\r\n\t<li>C++: <span style=\"color:#e74c3c;\"><code>std::cout &lt;&lt; std::flush<\/code><\/span><\/li>\r\n\t<li>Java: <span style=\"color:#e74c3c;\"><code>System.out.flush()<\/code><\/span><\/li>\r\n\t<li>Python: <span style=\"color:#e74c3c;\"><code>sys.stdout.flush()<\/code><\/span><\/li>\r\n<\/ul>\r\n\r\n<p>\uc774\uc678\uc758 \uc5b8\uc5b4\uc5d0 \ub300\ud574\uc11c\ub294 \uc5b8\uc5b4\ubcc4 \uba85\uc138\ub97c \ucc38\uace0\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>$1\\leq T\\leq 100$<\/li>\r\n\t<li>$1\\leq N\\leq 1\\ 000$<\/li>\r\n\t<li>$S_1=1$<\/li>\r\n\t<li>$1\\leq S_i\\leq 4$ $(2\\leq i\\leq N)$<\/li>\r\n\t<li>$S_i=1\\implies S_{i+1}\\in\\{1,2\\}$ $(1\\leq i&lt;N)$<\/li>\r\n\t<li>$S_i=2\\implies S_{i+1}\\in\\{2,3\\}$ $(1\\leq i&lt;N)$<\/li>\r\n\t<li>$S_i=3\\implies S_{i+1}\\in\\{3,4\\}$ $(1\\leq i&lt;N)$<\/li>\r\n\t<li>$S_i=4\\implies S_{i+1}\\in\\{4,1\\}$ $(1\\leq i&lt;N)$<\/li>\r\n\t<li>\ubaa8\ub4e0 \uc9c8\ubb38\uc5d0\uc11c $1\\leq l\\leq r\\leq N$\uc774\uc5b4\uc57c \ud55c\ub2e4.<\/li>\r\n\t<li>\uc778\ud130\ub799\ud130\ub294 \ube44\uc801\uc751\uc801\uc774\ub2e4. \uc218\uc5f4 $S$\ub294 \uc0ac\uc804\uc5d0 \uacb0\uc815\ub418\uc5b4 \uc788\uace0, \uc9c8\ubb38\uc5d0 \ub530\ub77c \ubcc0\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/li>\r\n<\/ul>\r\n","custom_interaction":"<p>\uccab \uc904\uc5d0\ub294 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uc218 $T$\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uc2dc\uc791\uc5d0 \uc218\uc5f4 $S$\uc758 \uae38\uc774\ub97c \ub098\ud0c0\ub0b4\ub294 \uc815\uc218 $N$\uc774 \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uc9c8\ubb38\uc744 \ud558\uae30 \uc704\ud574\uc11c\ub294 \ub2e4\uc74c \uc911 \ud558\ub098\uc758 \ud615\uc2dd\uc73c\ub85c \ucd9c\ub825\ud55c \ub4a4 <strong>\ubc84\ud37c\ub97c \ube44\uc6cc\uc57c \ud55c\ub2e4.<\/strong><\/p>\r\n\r\n<ul>\r\n\t<li><span style=\"color:#e74c3c;\"><code>count l r<\/code><\/span><\/li>\r\n\t<li><span style=\"color:#e74c3c;\"><code>diff l r<\/code><\/span><\/li>\r\n<\/ul>\r\n\r\n<p>\ub9cc\uc57d \uc9c8\ubb38\uc774 <span style=\"color:#e74c3c;\"><code>count<\/code><\/span>\ub77c\uba74, \uc785\ub825\uc73c\ub85c \ub124 \uc815\uc218\ub97c \uc785\ub825\ubc1b\uc544\uc57c \ud55c\ub2e4. \uc774 \ub124 \uac1c\uc758 \uc815\uc218\ub294 \uad6c\uac04 $[l,r]$\uc5d0\uc11c $1$, $2$, $3$, $4$\uc758 \uac1c\uc218\ub97c \uc624\ub984\ucc28\uc21c\uc73c\ub85c \uc815\ub82c\ud55c \ubc30\uc5f4\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub9cc\uc57d \uc9c8\ubb38\uc774 <span style=\"color:#e74c3c;\"><code>diff<\/code><\/span>\ub77c\uba74, \uc785\ub825\uc73c\ub85c \ud558\ub098\uc758 \uc815\uc218\ub97c \uc785\ub825\ubc1b\uc544\uc57c \ud55c\ub2e4. \uc774 \uc815\uc218\ub294 $l\\le i&lt;r$\uc774\uace0 $S_i\\neq S_{i+1}$\uc778 $i$\uc758 \uac1c\uc218\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n\r\n<p>\ub2f5\uc744 \uc54c\uc558\ub2e4\uba74, \ub2e4\uc74c\uacfc \uac19\uc740 \ud615\uc2dd\uc73c\ub85c \ucd9c\ub825\ud55c \ub4a4 <strong>\ubc84\ud37c\ub97c \ube44\uc6cc\uc57c \ud55c\ub2e4.<\/strong> \uc774\ub54c, <span style=\"color:#e74c3c;\"><code>c1<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>c2<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>c3<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>c4<\/code><\/span>\ub294 \uac01\uac01 \uc218\uc5f4 $S$\uc5d0\uc11c $1$, $2$, $3$, $4$\uc758 \uac1c\uc218\uc640 \uc77c\uce58\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li><span style=\"color:#e74c3c;\"><code>answer c1 c2 c3 c4<\/code><\/span><\/li>\r\n<\/ul>\r\n\r\n<p>\ub2f9\uc2e0\uc758 \ud504\ub85c\uadf8\ub7a8\uc774 \uc870\uac74\uc5d0 \ub9de\uc9c0 \uc54a\ub294 \uc9c8\ubb38\uc744 \ud558\uac70\ub098, \uc9c8\ubb38 \ud69f\uc218\ub97c \ucd08\uacfc\ud558\uac70\ub098, \uc9c1\uc804\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574 \uc81c\uc2dc\ud55c \ub2f5\uc774 \ud2c0\ub9b0 \uacbd\uc6b0 \uc9c8\ubb38\uc5d0 \ub300\ud55c \ub2f5, \ub610\ub294 $N$\uc758 \uac12 \ub300\uc2e0 $-1$\uc744 \uc785\ub825\ubc1b\uac8c \ub41c\ub2e4. \uc774 \uacbd\uc6b0\uc5d0 \ub2f9\uc2e0\uc758 \ud504\ub85c\uadf8\ub7a8\uc740 \uc989\uc2dc \uc885\ub8cc\ud574\uc57c \ud558\uace0, \ucc44\uc810 \uacb0\uacfc\ub294 &#39;\ud2c0\ub838\uc2b5\ub2c8\ub2e4&#39;\ub97c \ubc1b\uac8c \ub41c\ub2e4. \ub9cc\uc57d \ud504\ub85c\uadf8\ub7a8\uc774 \uace7\ubc14\ub85c \uc885\ub8cc\ud558\uc9c0 \uc54a\ub294\ub2e4\uba74 \uc608\uc0c1\uce58 \ubabb\ud55c \ucc44\uc810 \uacb0\uacfc\ub97c \ubc1b\uc744 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ud558\ub098\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub97c \ud574\uacb0\ud55c \ub4a4\uc5d0\ub3c4 \ub2f9\uc2e0\uc758 \ud504\ub85c\uadf8\ub7a8\uc740 \uace7\ubc14\ub85c \ub2e4\uc74c \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc9c4\ud589\ud574\uc57c \ud55c\ub2e4. \ubaa8\ub4e0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub97c \ud574\uacb0\ud55c \ub4a4 \ud504\ub85c\uadf8\ub7a8\uc740 \uc989\uc2dc \uc885\ub8cc\ub418\uc5b4\uc57c \ud55c\ub2e4.<\/p>\r\n","custom_scoring":"<p>\uc774 \ubb38\uc81c\uc758 \uc810\uc218\ub294 \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uc9c8\ubb38 \ud69f\uc218 \uc911 \ucd5c\ub313\uac12 $Q_{max}$\uc5d0 \ub530\ub77c \uacb0\uc815\ub41c\ub2e4. $\\lfloor x\\rfloor$\uc740 $x$ \uc774\ud558\uc758 \ucd5c\ub300 \uc815\uc218\uc774\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>$1000&lt;Q_{max}$ : $0$\uc810<\/li>\r\n\t<li>$100&lt;Q_{max}\\leq 1000$ : $10$\uc810<\/li>\r\n\t<li>$50&lt;Q_{max}\\leq 100$ : $\\lfloor 50-0.4Q_{max}\\rfloor$\uc810<\/li>\r\n\t<li>$30&lt;Q_{max}\\leq 50$ : $80-Q_{max}$\uc810<\/li>\r\n\t<li>$19&lt;Q_{max}\\leq 30$ : $\\lfloor 98-1.6Q_{max}\\rfloor$\uc810<\/li>\r\n\t<li>$Q_{max}=19$ : $70$\uc810<\/li>\r\n\t<li>$Q_{max}=18$ : $75$\uc810<\/li>\r\n\t<li>$Q_{max}=17$ : $82$\uc810<\/li>\r\n\t<li>$Q_{max}=16$ : $90$\uc810<\/li>\r\n\t<li>$Q_{max}\\leq 15$ : $100$\uc810<\/li>\r\n<\/ul>\r\n","sample_explain_1":"<p>\uc704 \uc608\uc81c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ud558\ub098\uc774\uace0, \uc815\ub2f5 \uc218\uc5f4\uc740&nbsp;$S=[1,1]$\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub2f9\uc2e0\uc758 \ud504\ub85c\uadf8\ub7a8\uc740 \uba3c\uc800 \uc218\uc5f4\uc758 \uae38\uc774 $N$\uc744 \uc785\ub825\ubc1b\ub294\ub2e4. \uc774 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0\uc11c \uc218\uc5f4 $S$\uc758 \uae38\uc774\ub294 $2$\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub2f9\uc2e0\uc758 \ud504\ub85c\uadf8\ub7a8\uc740 <span style=\"color:#e74c3c;\"><code>diff 1 2<\/code><\/span>\ub97c \ucd9c\ub825\ud574 \uc9c8\ubb38\ud55c\ub2e4. $1\\le i&lt;2$\uc774\uace0 $S_i\\neq S_{i+1}$\uc778 $i$\uac00 \uc5c6\uc73c\ubbc0\ub85c, \ub2f5\uc73c\ub85c \uc815\uc218 $0$\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2f9\uc2e0\uc758 \ud504\ub85c\uadf8\ub7a8\uc740 <span style=\"color:#e74c3c;\"><code>count 1 2<\/code><\/span>\ub97c \ucd9c\ub825\ud574 \uc9c8\ubb38\ud55c\ub2e4. \uc218\uc5f4\uc758 \uad6c\uac04 $[1,2]$\uc5d0\uc11c $1$, $2$, $3$, $4$\uc758 \uac1c\uc218\ub294 \uac01\uac01 $2$\uac1c, $0$\uac1c, $0$\uac1c, $0$\uac1c\uc774\ubbc0\ub85c, \ub2f5\uc73c\ub85c \ub124 \uc815\uc218 $0$, $0$, $0$, $2$\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2f9\uc2e0\uc758 \ud504\ub85c\uadf8\ub7a8\uc740 <span style=\"color:#e74c3c;\"><code>answer 2 0 0 0<\/code><\/span>\uc744 \ucd9c\ub825\ud55c\ub2e4. \uc774\uac83\uc740 $1$, $2$, $3$, $4$\uc758 \uac1c\uc218\uac00 \uac01\uac01 $2$\uac1c, $0$\uac1c, $0$\uac1c, $0$\uac1c\ub77c\ub294 \ub73b\uc774\ub2e4. \uc815\ub2f5\uc744 \ub9de\ud614\uc73c\ubbc0\ub85c \ud574\ub2f9 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uac00 \uc885\ub8cc\ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc8fc\uc5b4\uc9c4 \uc608\uc2dc\ub294 \uc785\ucd9c\ub825\uc774 \uc5b4\ub5a4 \ubc29\uc2dd\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c0\ub294\uc9c0 \uc774\ud574\ub97c \ub3d5\uae30 \uc704\ud574 \uc758\ub3c4\uc801\uc73c\ub85c \uac1c\ud589 \uac04\uaca9 \ub4f1\uc744 \uc870\uc808\ud55c \uac83\uc774\uba70, <strong>\uc2e4\uc81c \uc785\ucd9c\ub825\uc5d0\uc11c\ub294 \ube48 \uc904\uc744 \ucd9c\ub825\ud558\uc9c0 \ub9d0\uc544\uc57c \ud55c\ub2e4.<\/strong><\/p>\r\n"},{"problem_id":"31074","problem_lang":"1","title":"Singleplayer Game","description":"<p>This problem is an <strong>interactive<\/strong> problem.<\/p>\r\n\r\n<p>There is a sequence $S$ in which the values are hidden. You are to find some information about the sequence $S$. The length of the sequence $S$ is $N$, and the sequence meets the following conditions:<\/p>\r\n\r\n<ul>\r\n\t<li>All elements of $S$ are either $1$, $2$, $3$, or $4$.<\/li>\r\n\t<li>$S_1=1$.<\/li>\r\n\t<li>If $S_i=1$, then either $S_{i+1}=1$ or $S_{i+1}=2$ $(1\\le i&lt;N)$ holds.<\/li>\r\n\t<li>If $S_i=2$, then either $S_{i+1}=2$ or $S_{i+1}=3$ $(1\\le i&lt;N)$ holds.<\/li>\r\n\t<li>If $S_i=3$, then either $S_{i+1}=3$ or $S_{i+1}=4$ $(1\\le i&lt;N)$ holds.<\/li>\r\n\t<li>If $S_i=4$, then either $S_{i+1}=4$ or $S_{i+1}=1$ $(1\\le i&lt;N)$ holds.<\/li>\r\n<\/ul>\r\n\r\n<p>You can ask two types of queries about the sequence:<\/p>\r\n\r\n<ul>\r\n\t<li><span style=\"color:#e74c3c;\"><code>count l r<\/code><\/span>: ask for the numbers of $1$, $2$, $3$, $4$ in the interval $[l,r]$, <strong>sorted in ascending order<\/strong>.<\/li>\r\n\t<li><span style=\"color:#e74c3c;\"><code>diff l r<\/code><\/span>: ask for the number of $i$ which satisfies $l\\le i&lt;r$ and $S_i\\neq S_{i+1}$.<\/li>\r\n<\/ul>\r\n\r\n<p>Your goal is to find the <strong>numbers of each element<\/strong> $1$, $2$, $3$, and $4$ in the sequence $S$.<\/p>\r\n","input":"","output":"","hint":"<p>You can flush the output buffer by using the following methods:<\/p>\r\n\r\n<ul>\r\n\t<li>C: <span style=\"color:#e74c3c;\"><code>fflush(stdout)<\/code><\/span><\/li>\r\n\t<li>C++: <span style=\"color:#e74c3c;\"><code>std::cout &lt;&lt; std::flush<\/code><\/span><\/li>\r\n\t<li>Java: <span style=\"color:#e74c3c;\"><code>System.out.flush()<\/code><\/span><\/li>\r\n\t<li>Python: <span style=\"color:#e74c3c;\"><code>sys.stdout.flush()<\/code><\/span><\/li>\r\n<\/ul>\r\n\r\n<p>For other languages, you should refer to the language-specific specifications.<\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>$1\\leq T\\leq 100$<\/li>\r\n\t<li>$1\\leq N\\leq 1\\ 000$<\/li>\r\n\t<li>$S_1=1$<\/li>\r\n\t<li>$1\\leq S_i\\leq 4$ $(2\\leq i\\leq N)$<\/li>\r\n\t<li>$S_i=1\\implies S_{i+1}\\in\\{1,2\\}$ $(1\\leq i&lt;N)$<\/li>\r\n\t<li>$S_i=2\\implies S_{i+1}\\in\\{2,3\\}$ $(1\\leq i&lt;N)$<\/li>\r\n\t<li>$S_i=3\\implies S_{i+1}\\in\\{3,4\\}$ $(1\\leq i&lt;N)$<\/li>\r\n\t<li>$S_i=4\\implies S_{i+1}\\in\\{4,1\\}$ $(1\\leq i&lt;N)$<\/li>\r\n\t<li>For all queries, $1\\leq l\\leq r\\leq N$ should hold.<\/li>\r\n\t<li>The interactor is not adaptive. The sequence $S$ is fixed for each test case, and it does not change after queries are made.<\/li>\r\n<\/ul>\r\n","custom_interaction":"<p>The first line of the input consists of an integer $T$ &mdash; the number of test cases.<\/p>\r\n\r\n<p>At the beginning of each test case, the first line contains an integer $N$, representing the length of the sequence $S$.<\/p>\r\n\r\n<p>To ask queries, print your query in one of the following format. <strong>You have to flush your output buffer after printing each query.<\/strong><\/p>\r\n\r\n<ul>\r\n\t<li><span style=\"color:#e74c3c;\"><code>count l r<\/code><\/span><\/li>\r\n\t<li><span style=\"color:#e74c3c;\"><code>diff l r<\/code><\/span><\/li>\r\n<\/ul>\r\n\r\n<p>If you asked a <span style=\"color:#e74c3c;\"><code>count<\/code><\/span> query, you have to read four integers from the input. These four integers represent an array sorted in ascending order, indicating the numbers of $1$, $2$, $3$, $4$ within the range $[l,r]$.<\/p>\r\n\r\n<p>If you asked a <span style=\"color:#e74c3c;\"><code>diff<\/code><\/span> query, you have to read a single integer from the input. This integer represents the number of $i$ where $l\\le i&lt;r$ and $S_i\\neq S_{i+1}$.<\/p>\r\n\r\n<p>Once you have the answer, output it in the following format. <strong>You should flush your output buffer after printing the answer.<\/strong> Here, <span style=\"color:#e74c3c;\"><code>c1<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>c2<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>c3<\/code><\/span>, and <span style=\"color:#e74c3c;\"><code>c4<\/code><\/span> correspond to the numbers of $1$, $2$, $3$, and $4$ in the sequence $S$.<\/p>\r\n\r\n<ul>\r\n\t<li><span style=\"color:#e74c3c;\"><code>answer c1 c2 c3 c4<\/code><\/span><\/li>\r\n<\/ul>\r\n\r\n<p>If you receive the integer $-1$ instead of an answer or a valid value of $N$, it means your program has asked an invalid queries, has exceed the limit of queries, or has given an incorrect answer on the previous test case. Your program must terminate immediately to receive a Wrong Answer verdict. Otherwise you can get an arbitrary verdict because your solution will continue to read from a closed stream.<\/p>\r\n\r\n<p>After solving a test case, your program should move to the next one immediately. After solving all test cases, your program should be terminated immediately.<\/p>\r\n","custom_scoring":"<p>The score for this problem depends on the maximum number of queries in each test case, denoted as $Q_{max}$. The symbol $\\lfloor x\\rfloor$ represents the greatest integer less than or equal to $x$.<\/p>\r\n\r\n<ul>\r\n\t<li>$1000&lt;Q_{max}$ : $0$ points<\/li>\r\n\t<li>$100&lt;Q_{max}\\leq 1000$ : $10$ points<\/li>\r\n\t<li>$50&lt;Q_{max}\\leq 100$ : $\\lfloor 50-0.4Q_{max}\\rfloor$ points<\/li>\r\n\t<li>$30&lt;Q_{max}\\leq 50$ : $80-Q_{max}$ points<\/li>\r\n\t<li>$19&lt;Q_{max}\\leq 30$ : $\\lfloor 98-1.6Q_{max}\\rfloor$ points<\/li>\r\n\t<li>$Q_{max}=19$ : $70$ points<\/li>\r\n\t<li>$Q_{max}=18$ : $75$ points<\/li>\r\n\t<li>$Q_{max}=17$ : $82$ points<\/li>\r\n\t<li>$Q_{max}=16$ : $90$ points<\/li>\r\n\t<li>$Q_{max}\\leq 15$ : $100$ points<\/li>\r\n<\/ul>\r\n","sample_explain_1":"<p>The above example has only one test case, and the hidden sequence for the test case is $S=[1,1]$.<\/p>\r\n\r\n<p>First, your program reads the value of $N$ &mdash; the length of the sequence. In this test case, the length of the sequence $S$ is $2$.<\/p>\r\n\r\n<p>Your program prints <span style=\"color:#e74c3c;\"><code>diff 1 2<\/code><\/span> as a query. Since there are no $i$ such that $1\\le i&lt;2$ and $S_i\\neq S_{i+1}$ holds, you will read $0$ as the answer.<\/p>\r\n\r\n<p>Your program prints <span style=\"color:#e74c3c;\"><code>count 1 2<\/code><\/span> as a query. Since the numbers of $1$, $2$, $3$, and $4$ in the interval $[1,2]$ of the sequence is $2$, $0$, $0$, $0$, respectively, you will read four integers $0$, $0$, $0$, $2$ as the answer.<\/p>\r\n\r\n<p>Your program prints <span style=\"color:#e74c3c;\"><code>answer 2 0 0 0<\/code><\/span>. This means that the numbers of $1$, $2$, $3$, $4$ are $2$, $0$, $0$, $0$ respectively. Since the answer is correct, the test case ends.<\/p>\r\n\r\n<p>The provided example is intentionally adjusted line spacings to help understand the interaction process. <strong>In the actual interaction, you should not read or print any blank lines.<\/strong><\/p>\r\n"}]

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