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문제

상근이와 창영이는 수열 접기 게임을 해보려고 한다. 게임은 아래와 같이 진행된다.

  1. 2보다 크거나 같은 정수 하나를 임의로 고른다.
  2. 임의의 정수 N개로 이루어진 수열을 만든다.
  3. N이 2인 경우에는 단계 6으로 이동한다.
  4. 첫 번째 수를 N번째 수와 더하고, 두 번째 수를 N-1번째 수와 더하는 형식으로 수열을 접어 새로운 수열을 하나 만든다. N이 홀수인 경우에는 가운데 수를 자기 자신과 더한다. 아래 그림 1은 접는 과정을 나타낸다.
  5. N을 ceil(N/2)로 바꾸고, 단계 3으로 이동한다.
  6. 이제 수열에는 숫자 두 개가 포함되어 있다. 첫 번째 수가 두 번째 수보다 큰 경우에는 상근이가 이기고, 나머지 경우는 창영이가 이긴다.

그림 1.a 접기 전

그림 1.b 한 번 접고 난 후

그림 1.c 한 번 더 접고 난 후, 상근이가 이겼다!

정수 N개로 이루어진 수열이 주어졌을 때, 수열 접기 게임의 승자를 구하는 프로그램을 작성하시오.

입력

첫째 줄에 테스트 케이스의 개수 T (1 ≤ T ≤ 100)가 주어진다. 각 테스트 케이스의 첫째 줄에는 수열에 포함된 수의 개수 N (2 ≤ N ≤ 100)이 주어진다. 둘째 줄에는 수열이 주어진다. 수열을 이루는 숫자는 32비트 부호있는 정수범위이다.

출력

각 테스트 케이스마다 상근이가 이긴 경우에는 Alice, 창영이가 이긴 경우에는 Bob을 테스트 케이스 번호와 함께 출력한다.

예제 입력 1

2
5
2 5 10 3 -4
3
5 4 -3

예제 출력 1

Case #1: Alice
Case #2: Bob

힌트

[{"problem_id":"9358","problem_lang":"0","title":"\uc21c\uc5f4 \uc811\uae30 \uac8c\uc784","description":"<p>\uc0c1\uadfc\uc774\uc640 \ucc3d\uc601\uc774\ub294 \uc218\uc5f4 \uc811\uae30 \uac8c\uc784\uc744 \ud574\ubcf4\ub824\uace0 \ud55c\ub2e4. \uac8c\uc784\uc740 \uc544\ub798\uc640 \uac19\uc774 \uc9c4\ud589\ub41c\ub2e4.<\/p>\r\n\r\n<ol>\r\n\t<li>2\ubcf4\ub2e4 \ud06c\uac70\ub098 \uac19\uc740 \uc815\uc218 \ud558\ub098\ub97c \uc784\uc758\ub85c \uace0\ub978\ub2e4.<\/li>\r\n\t<li>\uc784\uc758\uc758 \uc815\uc218 N\uac1c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uc218\uc5f4\uc744 \ub9cc\ub4e0\ub2e4.<\/li>\r\n\t<li>N\uc774 2\uc778 \uacbd\uc6b0\uc5d0\ub294 \ub2e8\uacc4 6\uc73c\ub85c \uc774\ub3d9\ud55c\ub2e4.<\/li>\r\n\t<li>\uccab \ubc88\uc9f8 \uc218\ub97c N\ubc88\uc9f8 \uc218\uc640 \ub354\ud558\uace0, \ub450 \ubc88\uc9f8 \uc218\ub97c N-1\ubc88\uc9f8 \uc218\uc640 \ub354\ud558\ub294 \ud615\uc2dd\uc73c\ub85c \uc218\uc5f4\uc744 \uc811\uc5b4 \uc0c8\ub85c\uc6b4 \uc218\uc5f4\uc744 \ud558\ub098 \ub9cc\ub4e0\ub2e4. N\uc774 \ud640\uc218\uc778 \uacbd\uc6b0\uc5d0\ub294 \uac00\uc6b4\ub370 \uc218\ub97c \uc790\uae30 \uc790\uc2e0\uacfc \ub354\ud55c\ub2e4. \uc544\ub798 \uadf8\ub9bc 1\uc740 \uc811\ub294 \uacfc\uc815\uc744 \ub098\ud0c0\ub0b8\ub2e4.<\/li>\r\n\t<li>N\uc744 ceil(N\/2)\ub85c \ubc14\uafb8\uace0, \ub2e8\uacc4 3\uc73c\ub85c \uc774\ub3d9\ud55c\ub2e4.<\/li>\r\n\t<li>\uc774\uc81c \uc218\uc5f4\uc5d0\ub294 \uc22b\uc790 \ub450 \uac1c\uac00 \ud3ec\ud568\ub418\uc5b4 \uc788\ub2e4. \uccab \ubc88\uc9f8 \uc218\uac00 \ub450 \ubc88\uc9f8 \uc218\ubcf4\ub2e4 \ud070 \uacbd\uc6b0\uc5d0\ub294 \uc0c1\uadfc\uc774\uac00 \uc774\uae30\uace0, \ub098\uba38\uc9c0 \uacbd\uc6b0\ub294 \ucc3d\uc601\uc774\uac00 \uc774\uae34\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p style=\"text-align:center\"><img alt=\"\" src=\"\/upload\/images\/fold1.png\" style=\"height:201px; width:497px\" \/><\/p>\r\n\r\n<p style=\"text-align:center\">\uadf8\ub9bc 1.a \uc811\uae30 \uc804<\/p>\r\n\r\n<p style=\"text-align:center\"><img alt=\"\" src=\"\/upload\/images\/fold2.png\" style=\"height:133px; width:327px\" \/><\/p>\r\n\r\n<p style=\"text-align:center\">\uadf8\ub9bc 1.b \ud55c \ubc88 \uc811\uace0 \ub09c \ud6c4<\/p>\r\n\r\n<p style=\"text-align:center\"><img alt=\"\" src=\"\/upload\/images\/fold3.png\" style=\"height:124px; width:376px\" \/><\/p>\r\n\r\n<p style=\"text-align:center\">\uadf8\ub9bc 1.c \ud55c \ubc88 \ub354 \uc811\uace0 \ub09c \ud6c4, \uc0c1\uadfc\uc774\uac00 \uc774\uacbc\ub2e4!<\/p>\r\n\r\n<p>\uc815\uc218 N\uac1c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uc218\uc5f4\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc218\uc5f4 \uc811\uae30 \uac8c\uc784\uc758 \uc2b9\uc790\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 T (1 &le; T &le; 100)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 \uc218\uc5f4\uc5d0 \ud3ec\ud568\ub41c \uc218\uc758 \uac1c\uc218 N (2 &le; N &le; 100)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ub458\uc9f8 \uc904\uc5d0\ub294 \uc218\uc5f4\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \uc218\uc5f4\uc744 \uc774\ub8e8\ub294 \uc22b\uc790\ub294 32\ube44\ud2b8 \ubd80\ud638\uc788\ub294 \uc815\uc218\ubc94\uc704\uc774\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 \uc0c1\uadfc\uc774\uac00 \uc774\uae34 \uacbd\uc6b0\uc5d0\ub294 Alice, \ucc3d\uc601\uc774\uac00 \uc774\uae34 \uacbd\uc6b0\uc5d0\ub294 Bob\uc744 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \ubc88\ud638\uc640 \ud568\uaed8 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"9358","problem_lang":"1","title":"Sequence Folding","description":"<p>Alice and Bob are practicing hard for the new ICPC season. They hold many private contests where only the two of them compete against each other. They almost have identical knowledge and skills, the matter which results many times in ties in both the number of problems solved and in time penalty! To break the tie, Alice and Bob invented a tie breaker technique called sequence folding! The following are the steps of this technique:&nbsp;<\/p>\r\n\r\n<ol>\r\n\t<li>Generate a random integer N &gt;= 2.&nbsp;<\/li>\r\n\t<li>Generate a sequence of N random integers.&nbsp;<\/li>\r\n\t<li>If N = 2 go to step 6.&nbsp;<\/li>\r\n\t<li>Fold the sequence by adding the Nth element to the first, the N-1th element to the second and so on, if N is odd then the middle element is added to itself, figure 1 illustrates the folding process.&nbsp;<\/li>\r\n\t<li>Set N = ceil (N\/2) and go to step 3.&nbsp;<\/li>\r\n\t<li>The sequence now contains two numbers, if the first is greater than the second then Alice wins, otherwise Bob wins.<\/li>\r\n<\/ol>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"\/upload\/images\/fold1.png\" style=\"height:201px; text-align:center; width:497px\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">Figure 1.a Before Folding&nbsp;<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"\/upload\/images\/fold2.png\" style=\"height:133px; text-align:center; width:327px\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">Figure 1.b After one step of folding&nbsp;<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"\/upload\/images\/fold3.png\" style=\"height:124px; text-align:center; width:376px\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">Figure 1.c After two steps of folding, Alice wins!&nbsp;<\/p>\r\n\r\n<p>In this problem you&rsquo;re given the sequence of N integers and are asked determine the contest winner using the sequence folding tie breaker technique.&nbsp;<\/p>\r\n","input":"<p>The first line contains T (1 &lt;= T &lt;= 100), the number of test cases. The first line of each test case contains an integer (2 &lt;= N &lt;= 100), the number of elements of the sequence. The next line contains N space separated integers. The sum of any subset of the numbers fit in a 32 bit signed integer.&nbsp;<\/p>\r\n","output":"<p>For each test case print the name of the winner. Follow the output format below.&nbsp;<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]