{"raw_statement":[{"iden":"statement","content":"In the secret book of ACM, it’s said:_* “Glory for those who write short ICPC problems. May they live long, and never get Wrong Answers”* _.  Everyone likes problems with short statements. Right?  Let’s have five positive numbers: X1,X2,X3,X4,X5. We can form 10 distinct pairs of these five numbers. Given the sum of each one of the pairs, you are asked to find out the original five numbers.\n\nThe first line will be the number of test cases T.  Each test case is described in one line which contains 10 numbers, these are the sum of the two numbers in each pair. Notice that the input has no particular order, for example: the first number doesn’t have to be equal to {X1+ X2}.  All numbers are positive integers below 100,000,000.\n\nFor each test case, print one line which contains the number of the test case, and the five numbers X1,X2,X3,X4,X5 in ascending order, see the samples and follow the output format. There always exists a unique solution.\n\n"},{"iden":"input","content":"The first line will be the number of test cases T.  Each test case is described in one line which contains 10 numbers, these are the sum of the two numbers in each pair. Notice that the input has no particular order, for example: the first number doesn’t have to be equal to {X1+ X2}.  All numbers are positive integers below 100,000,000."},{"iden":"output","content":"For each test case, print one line which contains the number of the test case, and the five numbers X1,X2,X3,X4,X5 in ascending order, see the samples and follow the output format. There always exists a unique solution."},{"iden":"examples","content":"Input215 9 7 15 6 12 13 16 21 1412 18 13 10 17 20 21 15 16 14OutputCase 1: 2 4 5 10 11Case 2: 4 6 8 9 12"}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ T \\in \\mathbb{Z} $ be the number of test cases.  \nFor each test case, let $ S = \\{s_1, s_2, \\dots, s_{10}\\} $ be a multiset of 10 positive integers representing the pairwise sums of five unknown positive integers $ X = \\{x_1, x_2, x_3, x_4, x_5\\} $, where $ x_1 < x_2 < x_3 < x_4 < x_5 $.\n\n**Constraints**  \n1. $ 1 \\leq T \\leq \\text{unknown} $ (implied by input)  \n2. Each $ s_i \\in \\mathbb{Z}^+ $, $ s_i < 100{,}000{,}000 $  \n3. The multiset $ S $ consists exactly of the $ \\binom{5}{2} = 10 $ pairwise sums $ x_i + x_j $ for $ 1 \\leq i < j \\leq 5 $.  \n4. A unique solution $ (x_1, x_2, x_3, x_4, x_5) $ exists for each $ S $.\n\n**Objective**  \nFor each test case, recover the unique ordered tuple $ (x_1, x_2, x_3, x_4, x_5) $ such that $ x_1 < x_2 < x_3 < x_4 < x_5 $ and  \n$$\n\\{x_i + x_j \\mid 1 \\leq i < j \\leq 5\\} = S\n$$  \nOutput the tuple in ascending order.","simple_statement":"Given 10 numbers representing the sums of all pairs of 5 unknown positive numbers, find the original 5 numbers in ascending order.","has_page_source":false}