B. Olya and Game with Arraystime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputArtem suggested a game to the girl Olya. There is a list of n arrays, where the i-th array contains m_i \ge 2 positive integers a_{i,1}, a_{i,2}, \ldots, a_{i,m_i}.Olya can move at most one (possibly 0) integer from each array to another array. Note that integers can be moved from one array only once, but integers can be added to one array multiple times, and all the movements are done at the same time.The beauty of the list of arrays is defined as the sum \sum_{i=1}^n \min_{j=1}^{m_i} a_{i,j}. In other words, for each array, we find the minimum value in it and then sum up these values.The goal of the game is to maximize the beauty of the list of arrays. Help Olya win this challenging game!InputEach test consists of multiple test cases. The first line contains a single integer t (1 \le t \le 25000) — the number of test cases. The description of test cases follows.The first line of each test case contains a single integer n (1 \le n \le 25000) — the number of arrays in the list.This is followed by descriptions of the arrays. Each array description consists of two lines.The first line contains a single integer m_i (2 \le m_i \le 50000) — the number of elements in the i-th array.The next line contains m_i integers a_{i, 1}, a_{i, 2}, \ldots, a_{i, m_i} (1 \le a_{i,j} \le 10^9) — the elements of the i-th array.It is guaranteed that the sum of m_i over all test cases does not exceed 50000.OutputFor each test case, output a single line containing a single integer — the maximum beauty of the list of arrays that Olya can achieve.ExampleInput
3221 224 313100 1 6341001 7 1007 538 11 622 9Output
5
1
19
NoteIn the first test case, we can move the integer 3 from the second array to the first array. Then the beauty is \min(1, 2, 3) + \min(4) = 5. It can be shown that this is the maximum possible beauty.In the second test case, there is only one array, so regardless of the movements, the beauty will be \min(100, 1, 6) = 1.
3221 224 313100 1 6341001 7 1007 538 11 622 9
5 1 19 
['constructive algorithms', 'greedy', 'math', 'sortings', '*1000']