AT_arc211_a [ARC211A] Banned X 2

You are given a length- $ 9 $ sequence of non-negative integers $ A=(A_1,A_2,\dots,A_9) $ . It is guaranteed that $ 2\leq \sum_{i=1}^{9}A_i $ . You can perform the following operation any number of times (possibly zero): choose one element of $ A $ and add $ 1 $ to it. What is the minimum number of operations required so that there exists a sequence of positive integers $ S $ satisfying all of the following conditions? - All elements of $ S $ are between $ 1 $ and $ 9 $ , inclusive. - $ S $ contains exactly $ A_i $ occurrences of $ i $ for each integer $ i $ such that $ 1\leq i\leq 9 $ . (Thus, the length of $ S $ is $ \sum_{i=1}^{9}A_i $ .) - No two adjacent elements sum to $ 10 $ . It can be proved that the goal can be achieved in a finite number of operations. You are given $ T $ test cases; solve each of them.

The input is given from Standard Input in the following format: > $ T $ $ \text{case}_1 $ $ \text{case}_2 $ $ \vdots $ $ \text{case}_T $ Each test case is given in the following format: > $ A_1 $ $ A_2 $ $ \dots $ $ A_9 $

Output $ T $ lines. The $ i $ -th line should contain the answer for the $ i $ -th test case.

### Sample Explanation 1 For the first test case, initially, the possible values of $ S $ satisfying all conditions except the last one are $ (4,6) $ and $ (6,4) $ , neither of which satisfies the last condition. By choosing $ A_8 $ and adding $ 1 $ to it, $ S=(6,8,4) $ satisfies all conditions. For the second test case, $ S=(1,2,3,1) $ satisfies the conditions without any operations. ### Constraints - $ 1\leq T\leq 10^3 $ - $ 0\leq A_i\leq 10^9 $ $ (1\leq i\leq 9) $ - $ 2\leq \sum_{i=1}^{9}A_i $ - All input values are integers.