시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

길이 n인 음이 아닌 정수로 이루어진 배열 A에 대해, 0개 이상의 원소를 지워서 얻을 수 있는 배열을 "부분열"라고 한다.

배열 A의 부분열 S에 대해, S가 다음 조건을 만족하면 S를 A의 "홀수 부분열"이라고 정의한다:

  • S의 원소의 합의 자릿수 중 홀수인 것들이 홀수이다.

음이 아닌 정수 배열 A를 입력받아 A의 서로 다른 홀수 부분열의 개수를 출력하시오. 단, 부분열의 원소들을 정렬했을 시 그 결과가 같다면 같은 부분열로 취급한다.

A = [3, 3, 6, 8, 6] 경우 정답은 8이다.

  • 길이가 0인 홀수 부분열: X
  • 길이가 1인 홀수 부분열: [3]
    • 합이 3, 자릿수 중 홀수가 3으로 하나
  • 길이가 2인 홀수 부분열: [3, 6], [6, 6], [6, 8]
    • 합이 각각 9, 12, 14로 자릿수 중 홀수가 9, 1, 1로 하나씩
  • 길이가 3인 홀수 부분열: [3, 3, 6], [3, 3, 8]
  • 길이가 4인 홀수 부분열: [3, 3, 6, 6], [3, 6, 6, 8]
  • 길이가 5인 홀수 부분열: X

입력

첫 줄에 테스트 케이스의 수 T가 주어진다 (1 ≤ T ≤ 10).

각 테스트 케이스에 대해 첫 줄에 A의 길이 n 이 주어진다. 둘째 줄에 n개의 0이상의 정수가 공백으로 구분되어 주어진다. A의 각 원소는 0 이상 2,000 이하이다.

출력

각 테스트 케이스에 대해 홀수 부분열의 수를 한 줄에 출력한다.

서브태스크 1 (3점)

  • 1 ≤ n ≤ 10

서브태스크 2 (11점)

  • 1 ≤ n ≤ 60

예제 입력 1

3
3
3 3 6
4
0 1 2 3
5
3 3 6 8 6

예제 출력 1

3
8
8

힌트

  • 테스트 케이스 1: {3}, {3,6}, {3, 3, 6} 세 종류의 홀수-부분열이 있다.
  • 테스트 케이스 2: {1}, {3}, {0,1}, {0,3}, {1,2}, {2,3}, {0,1,2}, {0,2,3} 여덟 종류의 홀수-부분열이 있다.
  • 테스트 케이스 3: 문제에서 서술된대로 여덟 종류의 홀수-부분열이 있다.
[{"problem_id":"17279","problem_lang":"0","title":"\ud640\uc218 \ubd80\ubd84\uc5f4","description":"<p>\uae38\uc774 n\uc778 \uc74c\uc774 \uc544\ub2cc \uc815\uc218\ub85c \uc774\ub8e8\uc5b4\uc9c4 \ubc30\uc5f4 A\uc5d0 \ub300\ud574,&nbsp;0\uac1c \uc774\uc0c1\uc758 \uc6d0\uc18c\ub97c \uc9c0\uc6cc\uc11c \uc5bb\uc744 \uc218 \uc788\ub294 \ubc30\uc5f4\uc744 &quot;\ubd80\ubd84\uc5f4&quot;\ub77c\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ubc30\uc5f4 A\uc758 \ubd80\ubd84\uc5f4 S\uc5d0 \ub300\ud574, S\uac00 \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\ud558\uba74 S\ub97c A\uc758 &quot;\ud640\uc218 \ubd80\ubd84\uc5f4&quot;\uc774\ub77c\uace0 \uc815\uc758\ud55c\ub2e4:<\/p>\r\n\r\n<ul>\r\n\t<li>S\uc758 \uc6d0\uc18c\uc758 \ud569\uc758 \uc790\ub9bf\uc218 \uc911 \ud640\uc218\uc778 \uac83\ub4e4\uc774 \ud640\uc218\uc774\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc74c\uc774 \uc544\ub2cc \uc815\uc218 \ubc30\uc5f4 A\ub97c \uc785\ub825\ubc1b\uc544 A\uc758 \uc11c\ub85c \ub2e4\ub978 \ud640\uc218 \ubd80\ubd84\uc5f4\uc758 \uac1c\uc218\ub97c \ucd9c\ub825\ud558\uc2dc\uc624. \ub2e8, \ubd80\ubd84\uc5f4\uc758 \uc6d0\uc18c\ub4e4\uc744 \uc815\ub82c\ud588\uc744 \uc2dc \uadf8 \uacb0\uacfc\uac00 \uac19\ub2e4\uba74 \uac19\uc740 \ubd80\ubd84\uc5f4\ub85c \ucde8\uae09\ud55c\ub2e4.<\/p>\r\n\r\n<p>A = [3, 3, 6, 8, 6] \uacbd\uc6b0 \uc815\ub2f5\uc740 8\uc774\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uae38\uc774\uac00 0\uc778 \ud640\uc218 \ubd80\ubd84\uc5f4: X<\/li>\r\n\t<li>\uae38\uc774\uac00 1\uc778 \ud640\uc218 \ubd80\ubd84\uc5f4: [3]\r\n\t<ul>\r\n\t\t<li>\ud569\uc774 3, \uc790\ub9bf\uc218 \uc911 \ud640\uc218\uac00 3\uc73c\ub85c \ud558\ub098<\/li>\r\n\t<\/ul>\r\n\t<\/li>\r\n\t<li>\uae38\uc774\uac00 2\uc778 \ud640\uc218 \ubd80\ubd84\uc5f4: [3, 6], [6, 6], [6, 8]\r\n\t<ul>\r\n\t\t<li>\ud569\uc774 \uac01\uac01 9, 12, 14\ub85c \uc790\ub9bf\uc218 \uc911 \ud640\uc218\uac00 9, 1, 1\ub85c \ud558\ub098\uc529<\/li>\r\n\t<\/ul>\r\n\t<\/li>\r\n\t<li>\uae38\uc774\uac00 3\uc778 \ud640\uc218 \ubd80\ubd84\uc5f4: [3, 3, 6], [3, 3, 8]<\/li>\r\n\t<li>\uae38\uc774\uac00 4\uc778 \ud640\uc218 \ubd80\ubd84\uc5f4: [3, 3, 6, 6], [3, 6, 6, 8]<\/li>\r\n\t<li>\uae38\uc774\uac00 5\uc778 \ud640\uc218 \ubd80\ubd84\uc5f4: X<\/li>\r\n<\/ul>\r\n","input":"<p>\uccab \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4 (1 &le;&nbsp;T &le; 10).<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574 \uccab \uc904\uc5d0 A\uc758 \uae38\uc774 n \uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ub458\uc9f8 \uc904\uc5d0 n\uac1c\uc758 0\uc774\uc0c1\uc758 \uc815\uc218\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. A\uc758 \uac01 \uc6d0\uc18c\ub294 0 \uc774\uc0c1 2,000 \uc774\ud558\uc774\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574 \ud640\uc218 \ubd80\ubd84\uc5f4\uc758 \uc218\ub97c \ud55c \uc904\uc5d0 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<ul>\r\n\t<li>\ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 1: {3}, {3,6}, {3, 3, 6} \uc138 \uc885\ub958\uc758 \ud640\uc218-\ubd80\ubd84\uc5f4\uc774 \uc788\ub2e4.<\/li>\r\n\t<li>\ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 2: {1}, {3}, {0,1}, {0,3}, {1,2}, {2,3}, {0,1,2}, {0,2,3} \uc5ec\ub35f \uc885\ub958\uc758 \ud640\uc218-\ubd80\ubd84\uc5f4\uc774 \uc788\ub2e4.<\/li>\r\n\t<li>\ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 3: \ubb38\uc81c\uc5d0\uc11c \uc11c\uc220\ub41c\ub300\ub85c \uc5ec\ub35f \uc885\ub958\uc758 \ud640\uc218-\ubd80\ubd84\uc5f4\uc774 \uc788\ub2e4.<\/li>\r\n<\/ul>\r\n","original":"1","problem_lang_code":"\ud55c\uad6d\uc5b4","subtask1":"<ul>\r\n\t<li>1 &le; n &le; 10<\/li>\r\n<\/ul>\r\n","subtask2":"<ul>\r\n\t<li>1 &le; n &le; 60<\/li>\r\n<\/ul>\r\n"},{"problem_id":"17279","problem_lang":"1","title":"Odd Subsequences","description":"<p>A subsequence is a sequence that can be obtained from an array by deleting 0 or more elements. For a subsequence S of an array A with length n that consists of nonnegative integers, we define S as an &quot;odd-subsequence&quot; if it satisfies the following condition:<\/p>\r\n\r\n<ul>\r\n\t<li>Sum of elements of S has an odd number of its digits. The number of odd number(s) should be odd.<\/li>\r\n<\/ul>\r\n\r\n<p>Given a nonnegative integer array A, output the number of distinct odd subsequences of A. To be precise, we treat two subsequences as equivalent if their sorted results are equal.<\/p>\r\n\r\n<p>For instance, suppose A = [ 3, 3, 6, 8, 6 ].&nbsp;<\/p>\r\n\r\n<ul>\r\n\t<li>Odd subsequences of A with length 0 : -<\/li>\r\n\t<li>Odd subsequences of A with length 1 : [3]\r\n\t<ul>\r\n\t\t<li>The sum of elements is 3, which has a single odd digit 3<\/li>\r\n\t<\/ul>\r\n\t<\/li>\r\n\t<li>Odd subsequences of A with length 2 : [3, 6], [6, 6], [6, 8]\r\n\t<ul>\r\n\t\t<li>The sums of elements are 9, 12, 14 respectively, with single odd digit 9, 1, 1<\/li>\r\n\t<\/ul>\r\n\t<\/li>\r\n\t<li>Odd subsequences of A with length 3 : [3, 3, 6], [3, 3, 8]<\/li>\r\n\t<li>Odd subsequences of A with length 4 : [3, 3, 6, 6], [3, 6, 6, 8]<\/li>\r\n\t<li>Odd subsequences of A with length 5 : -<\/li>\r\n<\/ul>\r\n","input":"<p>The first line will contain an integer T (1 &le;&nbsp;T &le;&nbsp;10), the number of test cases.<\/p>\r\n\r\n<p>For each test case: The first line will contain n, and the second line will contain n non-negative integers describing A. Each element of A will be between 0 and 2,000.<\/p>\r\n","output":"<p>For each test case, output in a slinge line the number of odd subsequences you can make out of A.<\/p>\r\n","hint":"<ul>\r\n\t<li>Test case 1: {3}, {3,6}, and {3, 3, 6} are the only three odd subsequences&nbsp;of A.<\/li>\r\n\t<li>Test case 2: {1}, {3}, {0,1}, {0,3}, {1,2}, {2,3}, {0,1,2}, and {0,2,3} are the odd subsequences of A.<\/li>\r\n\t<li>Test case 3: 8 odd s of A were described in the problem statement.<\/li>\r\n<\/ul>\r\n","original":"0","problem_lang_code":"\uc601\uc5b4","subtask1":"<ul>\r\n\t<li>1 &le; n &le; 10<\/li>\r\n<\/ul>\r\n","subtask2":"<ul>\r\n\t<li>1 &le; n &le; 60<\/li>\r\n<\/ul>\r\n"}]

채점

  • 예제는 채점하지 않는다.