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문제

단백질은 아미노산의 연결체이다. 단백질은 이중 질량 분석기 (MS2)를 이용해서 단백질의 서열을 알아낼 수 있다.

문제를 풀기 위해 다음과 같은 상황을 가정한다.

  • 단백질은 최대 400개 아미노산이 연결된 형태이다.
  • 아미노산은 두 종류 P와 Q만 있다.
  • P의 질량은 97.05276돌턴, Q의 질량은 128.05858돌턴이다.

MS2의 결과는 실수의 집합이며, 각각의 실수는 피크라고 부른다. 집합은 단백질의 모든 prefix와 suffix의 질량이 포함(전체 단백질의 질량 포함)되어 있으며, 다른 숫자는 포함되어 있지 않다.

알 수 없는 단백질을 MS2로 실험한 결과가 주어진다. 실험은 오차가 발생할 수 있기 때문에, 결과는 아래 조건을 만족한다.

  • 일부 prefix와 suffix의 결과는 집합에 포함되어 있지 않다.
  • 단백질의 prefix/suffix 질량에 해당하지 않는 피크가 집합에 포함되어 있을 수도 있다. 이러한 피크를 노이즈 피크라고 한다.
  • 모든 피크는 양수이다.
  • 가장 큰 피크는 단백질 전체 질량이다.
  • prefix/suffix 질량에 해당하는 피크는 정확한 값이다.

실험 결과가 주어졌을 때, 최대 피크가 단백질의 질량이면서, 노이즈 피크의 수가 최소인 단백질을 만드는 프로그램을 작성하시오.

입력

첫째 줄에 MS2의 실험 결과인 피크의 수 n이 주어진다. (1 ≤ n ≤ 100,000)

다음 n개 줄에는 i번째 피크 pi가 주어진다.

항상 문제의 모든 조건을 만족시키며, 모든 피크는 다르다. 각 피크는 소수점 최대 5째자리까지 주어진다.

출력

길이가 최대 400인 P와 Q로 이루어진 문자열(단백질)을 출력한다. 노이즈 피크의 수를 최소로하는 답이 여러가지인 경우에는 아무거나 출력한다.

예제 입력 1

6
225.11134
353.16992
353.16991
291.15828
97.05276
128.05858

예제 출력 1

PQQ

힌트

가능한 단백질은 PQQ와 QQP이다. 두 단백질 모두 291.15828, 353.16991 결과를 제외하면 얻을 수 있다. 

[{"problem_id":"3998","problem_lang":"0","title":"\ub2e8\ubc31\uc9c8 \uc2dd\ubcc4","description":"<p>\ub2e8\ubc31\uc9c8\uc740 \uc544\ubbf8\ub178\uc0b0\uc758 \uc5f0\uacb0\uccb4\uc774\ub2e4. \ub2e8\ubc31\uc9c8\uc740 \uc774\uc911 \uc9c8\ub7c9 \ubd84\uc11d\uae30 (MS<sup>2<\/sup>)\ub97c \uc774\uc6a9\ud574\uc11c \ub2e8\ubc31\uc9c8\uc758 \uc11c\uc5f4\uc744 \uc54c\uc544\ub0bc \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ubb38\uc81c\ub97c \ud480\uae30 \uc704\ud574 \ub2e4\uc74c\uacfc \uac19\uc740 \uc0c1\ud669\uc744 \uac00\uc815\ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\ub2e8\ubc31\uc9c8\uc740 \ucd5c\ub300 400\uac1c \uc544\ubbf8\ub178\uc0b0\uc774 \uc5f0\uacb0\ub41c \ud615\ud0dc\uc774\ub2e4.<\/li>\r\n\t<li>\uc544\ubbf8\ub178\uc0b0\uc740 \ub450 \uc885\ub958 P\uc640 Q\ub9cc \uc788\ub2e4.<\/li>\r\n\t<li>P\uc758 \uc9c8\ub7c9\uc740 97.05276\ub3cc\ud134, Q\uc758 \uc9c8\ub7c9\uc740 128.05858\ub3cc\ud134\uc774\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>MS<sup>2<\/sup>\uc758 \uacb0\uacfc\ub294 \uc2e4\uc218\uc758 \uc9d1\ud569\uc774\uba70, \uac01\uac01\uc758 \uc2e4\uc218\ub294 \ud53c\ud06c\ub77c\uace0 \ubd80\ub978\ub2e4. \uc9d1\ud569\uc740 \ub2e8\ubc31\uc9c8\uc758 \ubaa8\ub4e0 prefix\uc640 suffix\uc758 \uc9c8\ub7c9\uc774 \ud3ec\ud568(\uc804\uccb4 \ub2e8\ubc31\uc9c8\uc758 \uc9c8\ub7c9 \ud3ec\ud568)\ub418\uc5b4 \uc788\uc73c\uba70, \ub2e4\ub978 \uc22b\uc790\ub294 \ud3ec\ud568\ub418\uc5b4 \uc788\uc9c0 \uc54a\ub2e4.<\/p>\r\n\r\n<p>\uc54c \uc218 \uc5c6\ub294 \ub2e8\ubc31\uc9c8\uc744 MS<sup>2<\/sup>\ub85c \uc2e4\ud5d8\ud55c \uacb0\uacfc\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc2e4\ud5d8\uc740 \uc624\ucc28\uac00 \ubc1c\uc0dd\ud560 \uc218 \uc788\uae30 \ub54c\ubb38\uc5d0, \uacb0\uacfc\ub294 \uc544\ub798 \uc870\uac74\uc744 \ub9cc\uc871\ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uc77c\ubd80 prefix\uc640 suffix\uc758 \uacb0\uacfc\ub294 \uc9d1\ud569\uc5d0 \ud3ec\ud568\ub418\uc5b4 \uc788\uc9c0 \uc54a\ub2e4.<\/li>\r\n\t<li>\ub2e8\ubc31\uc9c8\uc758 prefix\/suffix \uc9c8\ub7c9\uc5d0 \ud574\ub2f9\ud558\uc9c0 \uc54a\ub294 \ud53c\ud06c\uac00 \uc9d1\ud569\uc5d0 \ud3ec\ud568\ub418\uc5b4 \uc788\uc744 \uc218\ub3c4 \uc788\ub2e4. \uc774\ub7ec\ud55c \ud53c\ud06c\ub97c \ub178\uc774\uc988 \ud53c\ud06c\ub77c\uace0 \ud55c\ub2e4.<\/li>\r\n\t<li>\ubaa8\ub4e0 \ud53c\ud06c\ub294 \uc591\uc218\uc774\ub2e4.<\/li>\r\n\t<li>\uac00\uc7a5 \ud070 \ud53c\ud06c\ub294 \ub2e8\ubc31\uc9c8 \uc804\uccb4 \uc9c8\ub7c9\uc774\ub2e4.<\/li>\r\n\t<li>prefix\/suffix \uc9c8\ub7c9\uc5d0 \ud574\ub2f9\ud558\ub294 \ud53c\ud06c\ub294 \uc815\ud655\ud55c \uac12\uc774\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc2e4\ud5d8 \uacb0\uacfc\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ucd5c\ub300 \ud53c\ud06c\uac00 \ub2e8\ubc31\uc9c8\uc758 \uc9c8\ub7c9\uc774\uba74\uc11c, \ub178\uc774\uc988 \ud53c\ud06c\uc758 \uc218\uac00 \ucd5c\uc18c\uc778 \ub2e8\ubc31\uc9c8\uc744 \ub9cc\ub4dc\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 MS2\uc758 \uc2e4\ud5d8 \uacb0\uacfc\uc778 \ud53c\ud06c\uc758 \uc218 n\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; n &le; 100,000)<\/p>\r\n\r\n<p>\ub2e4\uc74c n\uac1c \uc904\uc5d0\ub294 i\ubc88\uc9f8 \ud53c\ud06c p<sub>i<\/sub>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ud56d\uc0c1 \ubb38\uc81c\uc758 \ubaa8\ub4e0 \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a4\uba70, \ubaa8\ub4e0 \ud53c\ud06c\ub294 \ub2e4\ub974\ub2e4. \uac01 \ud53c\ud06c\ub294 \uc18c\uc218\uc810 \ucd5c\ub300 5\uc9f8\uc790\ub9ac\uae4c\uc9c0 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uae38\uc774\uac00 \ucd5c\ub300 400\uc778 P\uc640 Q\ub85c \uc774\ub8e8\uc5b4\uc9c4 \ubb38\uc790\uc5f4(\ub2e8\ubc31\uc9c8)\uc744 \ucd9c\ub825\ud55c\ub2e4. \ub178\uc774\uc988 \ud53c\ud06c\uc758 \uc218\ub97c \ucd5c\uc18c\ub85c\ud558\ub294 \ub2f5\uc774 \uc5ec\ub7ec\uac00\uc9c0\uc778 \uacbd\uc6b0\uc5d0\ub294 \uc544\ubb34\uac70\ub098 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\uac00\ub2a5\ud55c \ub2e8\ubc31\uc9c8\uc740 PQQ\uc640 QQP\uc774\ub2e4. \ub450 \ub2e8\ubc31\uc9c8 \ubaa8\ub450 291.15828, 353.16991 \uacb0\uacfc\ub97c \uc81c\uc678\ud558\uba74 \uc5bb\uc744 \uc218 \uc788\ub2e4.&nbsp;<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"3998","problem_lang":"1","title":"Identification of Protein","description":"<p>A protein is a sequence of amino acids. One of the ways to sequence (i.e. to read) a protein is to use Tandem mass spectrometry (usually abbreviated as MS<sup>2<\/sup>).<\/p>\r\n\r\n<p>In this problem the following toy situation is considered:<\/p>\r\n\r\n<ul>\r\n\t<li>A protein is a sequence of at most 400 amino acids.<\/li>\r\n\t<li>The are only two types of amino acids, P and Q.<\/li>\r\n\t<li>Mass of P is 97.05276 daltons, mass of Q is 128.05858 daltons.<\/li>\r\n<\/ul>\r\n\r\n<p>The result of an ideal measurement via MS<sup>2<\/sup> is a set of real numbers called peaks, which contains the mass of each pre\ufb01x and each su\ufb03x of the protein (including the entire protein), and no other numbers.<\/p>\r\n\r\n<p>But it&rsquo;s never ideal in practice. You&rsquo;re given the results of MS<sup>2<\/sup> experiment for an unknown protein. The following conditions hold:<\/p>\r\n\r\n<ul>\r\n\t<li>masses of some pre\ufb01xes and\/or some su\ufb03xes might be absent in the set.<\/li>\r\n\t<li>some peaks that do not correspond to any pre\ufb01x\/su\ufb03x mass might be included in the set (they are called noise peaks).<\/li>\r\n\t<li>all peaks are positive numbers.<\/li>\r\n\t<li>the largest peak in the set is equal to the mass of the entire protein.<\/li>\r\n\t<li>all peaks that correspond to pre\ufb01x\/su\ufb03x masses are exact measurements.<\/li>\r\n<\/ul>\r\n\r\n<p>Reconstruct the protein that has the mass equal to the largest peak and minimizes the number of noise peaks (and thus maximizes the number of peaks that correspond to its su\ufb03xes or pre\ufb01xes).<\/p>\r\n","input":"<p>The \ufb01rst line contains integer n (1 &le; n &le; 100 000), the number of peaks in the given MS<sup>2<\/sup> experiment results.<\/p>\r\n\r\n<p>Each of the next n lines contains a positive real number p<sub>i<\/sub>, the mass of the i-th peak.<\/p>\r\n\r\n<p>All of above conditions are guaranteed to be satis\ufb01ed. All peaks are distinct. Each peak has no more than 5 digits after a decimal point.<\/p>\r\n","output":"<p>Output a string of up to 400 characters consisting only of &lsquo;P&rsquo; and &lsquo;Q&rsquo; characters &mdash; the reconstructed protein. If there are multiple answers that minimize the number of noise peaks, output any one of them.<\/p>\r\n","hint":"<p>In the given example, the protein PQQ (or QQP) explains all peaks except two: 291.15828 and 353.16991.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]