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문제

상근이가 1학년 때, 덧셈, 뺄셈을 매우 좋아했다. 상근이는 숫자가 줄 지어있는 것을 보기만 하면, 마지막 두 숫자 사이에 '='을 넣고, 나머지 숫자 사이에는 '+' 또는 '-'를 넣어 등식을 만들며 놀고 있다. 예를 들어, "8 3 2 4 8 7 2 4 0 8 8"에서 등식 "8+3-2-4+8-7-2-4-0+8=8"을 만들 수 있다.

상근이는 올바른 등식을 만들려고 한다. 상근이는 아직 학교에서 음수를 배우지 않았고, 20을 넘는 수는 모른다. 따라서, 왼쪽부터 계산할 때, 중간에 나오는 수가 모두 0 이상 20 이하이어야 한다. 예를 들어, "8+3+2-4-8-7+2+4+0+8=8"은 올바른 등식이지만, 8+3+2-4-8-7이 음수이기 때문에, 상근이가 만들 수 없는 등식이다.

숫자가 주어졌을 때, 상근이가 만들 수 있는 올바른 등식의 수를 구하는 프로그램을 작성하시오.

입력

첫째 줄에 숫자의 개수 N이 주어진다. (3 ≤ N ≤ 100) 둘째 줄에는 0 이상 9 이하의 정수 N개가 공백으로 구분해 주어진다.

출력

첫째 줄에 상근이가 만들 수 있는 올바른 등식의 개수를 출력한다. 이 값은 263-1 이하이다.

예제 입력 1

11
8 3 2 4 8 7 2 4 0 8 8

예제 출력 1

10

예제 입력 2

40
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1

예제 출력 2

7069052760

힌트

예제 1의 경우 다음과 같이 10가지 방법이 있다.

  • 8+3-2-4+8-7-2-4-0+8=8
  • 8+3-2-4+8-7-2-4+0+8=8
  • 8+3+2+4-8-7+2-4-0+8=8
  • 8+3+2+4-8-7+2-4+0+8=8
  • 8+3+2-4+8-7+2+4-0-8=8
  • 8+3+2-4+8-7+2+4+0-8=8
  • 8-3+2+4-8+7+2+4-0-8=8
  • 8-3+2+4-8+7+2+4+0-8=8
  • 8-3+2-4+8+7+2-4-0-8=8
  • 8-3+2-4+8+7+2-4+0-8=8
[{"problem_id":"5557","problem_lang":"0","title":"1\ud559\ub144","description":"<p>\uc0c1\uadfc\uc774\uac00 1\ud559\ub144 \ub54c, \ub367\uc148, \ube84\uc148\uc744 \ub9e4\uc6b0 \uc88b\uc544\ud588\ub2e4. \uc0c1\uadfc\uc774\ub294 \uc22b\uc790\uac00 \uc904 \uc9c0\uc5b4\uc788\ub294 \uac83\uc744 \ubcf4\uae30\ub9cc \ud558\uba74, \ub9c8\uc9c0\ub9c9 \ub450 \uc22b\uc790 \uc0ac\uc774\uc5d0 &#39;=&#39;\uc744 \ub123\uace0, \ub098\uba38\uc9c0 \uc22b\uc790 \uc0ac\uc774\uc5d0\ub294 &#39;+&#39; \ub610\ub294 &#39;-&#39;\ub97c \ub123\uc5b4 \ub4f1\uc2dd\uc744 \ub9cc\ub4e4\uba70 \ub180\uace0 \uc788\ub2e4. \uc608\ub97c \ub4e4\uc5b4, &quot;8 3 2 4 8 7 2 4 0 8 8&quot;\uc5d0\uc11c \ub4f1\uc2dd &quot;8+3-2-4+8-7-2-4-0+8=8&quot;\uc744 \ub9cc\ub4e4 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc0c1\uadfc\uc774\ub294 \uc62c\ubc14\ub978 \ub4f1\uc2dd\uc744 \ub9cc\ub4e4\ub824\uace0 \ud55c\ub2e4. \uc0c1\uadfc\uc774\ub294 \uc544\uc9c1 \ud559\uad50\uc5d0\uc11c \uc74c\uc218\ub97c \ubc30\uc6b0\uc9c0 \uc54a\uc558\uace0, 20\uc744 \ub118\ub294 \uc218\ub294 \ubaa8\ub978\ub2e4. \ub530\ub77c\uc11c, \uc67c\ucabd\ubd80\ud130 \uacc4\uc0b0\ud560 \ub54c, \uc911\uac04\uc5d0 \ub098\uc624\ub294 \uc218\uac00 \ubaa8\ub450 0 \uc774\uc0c1 20 \uc774\ud558\uc774\uc5b4\uc57c \ud55c\ub2e4. \uc608\ub97c \ub4e4\uc5b4, &quot;8+3+2-4-8-7+2+4+0+8=8&quot;\uc740 \uc62c\ubc14\ub978 \ub4f1\uc2dd\uc774\uc9c0\ub9cc, 8+3+2-4-8-7\uc774 \uc74c\uc218\uc774\uae30 \ub54c\ubb38\uc5d0, \uc0c1\uadfc\uc774\uac00 \ub9cc\ub4e4 \uc218 \uc5c6\ub294 \ub4f1\uc2dd\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc22b\uc790\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc0c1\uadfc\uc774\uac00 \ub9cc\ub4e4 \uc218 \uc788\ub294 \uc62c\ubc14\ub978 \ub4f1\uc2dd\uc758 \uc218\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc22b\uc790\uc758 \uac1c\uc218 N\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (3 &le; N &le; 100) \ub458\uc9f8 \uc904\uc5d0\ub294 0 \uc774\uc0c1 9 \uc774\ud558\uc758 \uc815\uc218 N\uac1c\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ud574 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc0c1\uadfc\uc774\uac00 \ub9cc\ub4e4 \uc218 \uc788\ub294 \uc62c\ubc14\ub978 \ub4f1\uc2dd\uc758 \uac1c\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4. \uc774 \uac12\uc740 2<sup>63<\/sup>-1 \uc774\ud558\uc774\ub2e4.<\/p>\r\n","hint":"<p>\uc608\uc81c 1\uc758 \uacbd\uc6b0 \ub2e4\uc74c\uacfc \uac19\uc774 10\uac00\uc9c0 \ubc29\ubc95\uc774 \uc788\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>8+3-2-4+8-7-2-4-0+8=8<\/li>\r\n\t<li>8+3-2-4+8-7-2-4+0+8=8<\/li>\r\n\t<li>8+3+2+4-8-7+2-4-0+8=8<\/li>\r\n\t<li>8+3+2+4-8-7+2-4+0+8=8<\/li>\r\n\t<li>8+3+2-4+8-7+2+4-0-8=8<\/li>\r\n\t<li>8+3+2-4+8-7+2+4+0-8=8<\/li>\r\n\t<li>8-3+2+4-8+7+2+4-0-8=8<\/li>\r\n\t<li>8-3+2+4-8+7+2+4+0-8=8<\/li>\r\n\t<li>8-3+2-4+8+7+2-4-0-8=8<\/li>\r\n\t<li>8-3+2-4+8+7+2-4+0-8=8<\/li>\r\n<\/ul>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"5557","problem_lang":"2","title":"1\u5e74\u751f (A First Grader)","description":"<p>JOI\u541b\u306f\u5c0f\u5b66 1 \u5e74\u751f\u3067\u3042\u308b\uff0eJOI\u541b\u306f\u6559\u308f\u3063\u305f\u3070\u304b\u308a\u306e\u8db3\u3057\u7b97\uff0c\u5f15\u304d\u7b97\u304c\u3068\u3066\u3082\u597d\u304d\u3067\uff0c\u6570\u5b57\u304c\u4e26\u3093\u3067\u3044\u308b\u306e\u3092\u898b\u308b\u3068\u6700\u5f8c\u306e 2 \u3064\u306e\u6570\u5b57\u306e\u9593\u306b\u300c=\u300d\u3092\u5165\u308c\uff0c\u6b8b\u308a\u306e\u6570\u5b57\u306e\u9593\u306b\u5fc5\u305a\u300c+\u300d\u307e\u305f\u306f\u300c-\u300d\u3092\u5165\u308c\u3066\u7b49\u5f0f\u3092\u4f5c\u3063\u3066\u904a\u3093\u3067\u3044\u308b\uff0e\u4f8b\u3048\u3070\u300c8 3 2 4 8 7 2 4 0 8 8\u300d\u304b\u3089\uff0c\u7b49\u5f0f\u300c8+3-2-4+8-7-2-4-0+8=8\u300d\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e<\/p>\r\n\r\n<p>JOI\u541b\u306f\u7b49\u5f0f\u3092\u4f5c\u3063\u305f\u5f8c\uff0c\u305d\u308c\u304c\u6b63\u3057\u3044\u7b49\u5f0f\u306b\u306a\u3063\u3066\u3044\u308b\u304b\u3092\u8a08\u7b97\u3057\u3066\u78ba\u304b\u3081\u308b\uff0e\u305f\u3060\u3057\uff0cJOI\u541b\u306f\u307e\u3060\u8ca0\u306e\u6570\u306f\u77e5\u3089\u306a\u3044\u3057\uff0c20 \u3092\u8d85\u3048\u308b\u6570\u306e\u8a08\u7b97\u306f\u3067\u304d\u306a\u3044\uff0e\u3057\u305f\u304c\u3063\u3066\uff0c\u6b63\u3057\u3044\u7b49\u5f0f\u306e\u3046\u3061\u5de6\u8fba\u3092\u5de6\u304b\u3089\u8a08\u7b97\u3057\u305f\u3068\u304d\u8a08\u7b97\u306e\u9014\u4e2d\u3067\u73fe\u308c\u308b\u6570\u304c\u5168\u3066 0 \u4ee5\u4e0a 20 \u4ee5\u4e0b\u306e\u7b49\u5f0f\u3060\u3051\u304cJOI\u541b\u304c\u78ba\u304b\u3081\u3089\u308c\u308b\u6b63\u3057\u3044\u7b49\u5f0f\u3067\u3042\u308b\uff0e\u4f8b\u3048\u3070\uff0c\u300c8+3+2-4-8-7+2+4+0+8=8\u300d\u306f \u6b63\u3057\u3044\u7b49\u5f0f\u3060\u304c\uff0c\u9014\u4e2d\u306b\u73fe\u308c\u308b 8+3-2-4-8-7 \u304c\u8ca0\u306e\u6570\u306a\u306e\u3067JOI\u541b\u306f\u3053\u306e\u7b49\u5f0f\u304c\u6b63\u3057\u3044\u304b\u3069\u3046\u304b\u78ba\u304b\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u3044\uff0e<\/p>\r\n\r\n<p>\u5165\u529b\u3068\u3057\u3066\u6570\u5b57\u306e\u5217\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\uff0cJOI\u541b\u304c\u4f5c\u308a\uff0c\u78ba\u304b\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u6b63\u3057\u3044\u7b49\u5f0f\u306e\u500b\u6570\u3092\u6c42\u3081\u308b\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4f5c\u6210\u305b\u3088\uff0e<\/p>\r\n","input":"<p>\u5165\u529b\u30d5\u30a1\u30a4\u30eb\u306f 2 \u884c\u304b\u3089\u306a\u308b\uff0e1 \u884c\u76ee\u306b\u306f\u4e26\u3093\u3067\u3044\u308b\u6570\u5b57\u306e\u500b\u6570\u3092\u8868\u3059\u6574\u6570 N \uff083 \u2266 N \u2266 100\uff09\u304c\u66f8\u304b\u308c\u3066\u3044\u308b\uff0e2 \u884c\u76ee\u306b\u306f 0 \u4ee5\u4e0a 9 \u4ee5\u4e0b\u306e\u6574\u6570\u304c N \u500b\uff0c\u7a7a\u767d\u3092\u533a\u5207\u308a\u3068\u3057\u3066\u66f8\u304b\u308c\u3066\u3044\u308b\uff0e<\/p>\r\n\r\n<p>\u4e0e\u3048\u3089\u308c\u308b\u5165\u529b\u30c7\u30fc\u30bf\u306e 60% \u3067\u306f\uff0cJOI\u541b\u304c\u4f5c\u308a\uff0c\u78ba\u304b\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u6b63\u3057\u3044\u7b49\u5f0f\u306e\u500b\u6570\u306f 2<sup>31<\/sup>-1 \u3092\u8d85\u3048\u306a\u3044\uff0e\u307e\u305f\uff0c\u4e0e\u3048\u3089\u308c\u308b\u5165\u529b\u30c7\u30fc\u30bf\u306e\u5168\u3066\u306b\u304a\u3044\u3066\uff0cJOI\u541b\u304c\u4f5c\u308a\uff0c\u78ba\u304b\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u6b63\u3057\u3044\u7b49\u5f0f\u306e\u500b\u6570\u306f 2<sup>63<\/sup>-1 \u3092\u8d85\u3048\u306a\u3044\uff0e<\/p>\r\n","output":"<p>JOI\u541b\u304c\u4f5c\u308a\uff0c\u78ba\u304b\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u6b63\u3057\u3044\u7b49\u5f0f\u306e\u500b\u6570\u3092\u8868\u3059\u6574\u6570\u3092 1 \u884c\u3067\u51fa\u529b\u305b\u3088\uff0e<\/p>\r\n","hint":"<p>\u5165\u529b\u4f8b 1 \u306b\u304a\u3044\u3066\uff0cJOI\u541b\u306f 10 \u500b\u306e\u6b63\u3057\u3044\u7b49\u5f0f<\/p>\r\n\r\n<ul>\r\n\t<li>8+3-2-4+8-7-2-4-0+8=8<\/li>\r\n\t<li>8+3-2-4+8-7-2-4+0+8=8<\/li>\r\n\t<li>8+3+2+4-8-7+2-4-0+8=8<\/li>\r\n\t<li>8+3+2+4-8-7+2-4+0+8=8<\/li>\r\n\t<li>8+3+2-4+8-7+2+4-0-8=8<\/li>\r\n\t<li>8+3+2-4+8-7+2+4+0-8=8<\/li>\r\n\t<li>8-3+2+4-8+7+2+4-0-8=8<\/li>\r\n\t<li>8-3+2+4-8+7+2+4+0-8=8<\/li>\r\n\t<li>8-3+2-4+8+7+2-4-0-8=8<\/li>\r\n\t<li>8-3+2-4+8+7+2-4+0-8=8<\/li>\r\n<\/ul>\r\n\r\n<p>\u3092\u4f5c\u308a\uff0c\u78ba\u304b\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u3067 10 \u3092\u51fa\u529b\u3059\u308b\uff0e<\/p>\r\n\r\n<p>\u5165\u529b\u4f8b 2 \u306b\u304a\u3044\u3066\uff0c\u7b54\u3048\u304c 32 bit\u7b26\u53f7\u4ed8\u304d\u6574\u6570\u306e\u7bc4\u56f2\u306b\u53ce\u307e\u3089\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u305b\u3088\uff0e<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"Japanese"}]

출처

Olympiad > Japanese Olympiad in Informatics > Japanese Olympiad in Informatics Qualification Round > JOI 2011 예선 4번

  • 문제를 번역한 사람: baekjoon
  • 데이터를 추가한 사람: eovh1962
  • 어색한 표현을 찾은 사람: mwy3055
  • 문제의 오타를 찾은 사람: rim