CF1747A Two Groups

You are given an array $ a $ consisting of $ n $ integers. You want to distribute these $ n $ integers into two groups $ s_1 $ and $ s_2 $ (groups can be empty) so that the following conditions are satisfied: - For each $ i $ $ (1 \leq i \leq n) $ , $ a_i $ goes into exactly one group. - The value $ |sum(s_1)| - |sum(s_2)| $ is the maximum possible among all such ways to distribute the integers.Here $ sum(s_1) $ denotes the sum of the numbers in the group $ s_1 $ , and $ sum(s_2) $ denotes the sum of the numbers in the group $ s_2 $ . Determine the maximum possible value of $ |sum(s_1)| - |sum(s_2)| $ .

The input consists of multiple test cases. The first line contains a single integer $ t $ $ (1 \leq t \leq 2 \cdot 10^4) $ — the number of test cases. The description of the test cases follows. The first line of each test case contains a single integer $ n $ $ (1 \leq n \leq 10^5) $ — the length of the array $ a $ . The second line of each test case contains $ n $ integers $ a_1,a_2 \ldots a_n $ $ (-10^9 \leq a_i \leq 10^9) $ — elements of the array $ a $ . It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2\cdot 10^5 $ .

For each test case, output a single integer — the maximum possible value of $ |sum(s_1)| - |sum(s_2)| $ .

In the first testcase, we can distribute as $ s_1 = \{10\} $ , $ s_2 = \{-10\} $ . Then the value will be $ |10| - |-10| = 0 $ . In the second testcase, we can distribute as $ s_1 = \{0, 11, -1\} $ , $ s_2 = \{-2\} $ . Then the value will be $ |0 + 11 - 1| - |-2| = 10 - 2 = 8 $ . In the third testcase, we can distribute as $ s_1 = \{2, 3, 2\} $ , $ s_2 = \{\} $ . Then the value will be $ |2 + 3 + 2| - |0| = 7 $ . In the fourth testcase, we can distribute as $ s_1 = \{-9, -4, 0\} $ , $ s_2 = \{2, 0\} $ . Then the value will be $ |-9 - 4 + 0| - |2 + 0| = 13 - 2 = 11 $ .