CF2266A Good Contest

The next programming contest has three problems and $ n $ participants. Problem $ 1 $ is easy, problem $ 2 $ is medium, and problem $ 3 $ is hard. A participant is called weak if they did not solve all three problems. Unfortunately, the scoreboard was lost. The only remaining information is an array $ a $ of length $ 3 $ , where $ a_i $ is the number of participants who solved problem $ i $ . Among all scoreboards consistent with this information, find the minimum possible number of weak participants.

The first line contains an integer $ t $ ( $ 1 \le t \le 3000 $ ) — the number of test cases. The first line of each test case contains an integer $ n $ ( $ 1 \le n \le 9 $ ) — the number of participants. The second line of each test case contains three integers $ a_1, a_2, a_3 $ ( $ 0 \le a_i \le n $ ), where $ a_i $ is the number of participants who solved problem $ i $ .

For each test case, print a single integer — the minimum possible number of weak participants.

In the first test case, all $ 3 $ participants can have solved all three problems, so the answer is $ 0 $ . In the second test case, participant $ 1 $ could have solved only problems $ 1 $ and $ 2 $ , while participants $ 2 $ , $ 3 $ , and $ 4 $ solved all three problems. Therefore, participant $ 1 $ is the only participant who is weak, so the answer is $ 1 $ . It can be shown that this is minimal.