B. Divan and a New Project time limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe company "Divan's Sofas" is planning to build n + 1 different buildings on a coordinate line so that:   the coordinate of each building is an integer number;  no two buildings stand at the same point. Let x_i be the coordinate of the i-th building. To get from the building i to the building j, Divan spends |x_i - x_j| minutes, where |y| is the absolute value of y.All buildings that Divan is going to build can be numbered from 0 to n. The businessman will live in the building 0, the new headquarters of "Divan's Sofas". In the first ten years after construction Divan will visit the i-th building a_i times, each time spending 2 \cdot |x_0-x_i| minutes for walking.Divan asks you to choose the coordinates for all n + 1 buildings so that over the next ten years the businessman will spend as little time for walking as possible.InputEach test contains several test cases. The first line contains one integer number t (1 \le t \le 10^3) — the number of test cases.The first line of each case contains an integer n (1 \le n \le 2 \cdot 10^5) — the number of buildings that "Divan's Sofas" is going to build, apart from the headquarters.The second line contains the sequence a_1, a_2, \ldots, a_n (0 \le a_i \le 10^6), where a_i is the number of visits to the i-th building.It is guaranteed that the sum of n over all test cases does not exceed 2 \cdot 10^5.OutputFor each test case, on the first line print the number T — the minimum time Divan will spend walking. On the second line print the sequence x_0, x_1, \ldots, x_n of n + 1 integers, where x_i (-10^6 \le x_i \le 10^6) is the selected coordinate of the i-th building. It can be shown that an optimal answer exists with coordinates not exceeding 10^6.If there are multiple answers, print any of them.ExampleInput
4
3
1 2 3
5
3 8 10 6 1
5
1 1 1 1 1
1
0
Output
14
2 4 1 3
78
1 -1 0 2 3 4
18
3 6 1 5 2 4
0
1 2NoteLet's look at the first example.Divan will visit the first building a_1 = 1 times, the second a_2 = 2 times and the third a_3 = 3 times. Then one of the optimal solution will be as follows:   the headquarters is located in x_0 = 2;  x_1 = 4: Divan will spend 2 \cdot |x_0-x_1| \cdot a_1 = 2 \cdot |2-4| \cdot 1 = 4 minutes walking to the first building;  x_2 = 1: Divan will spend 2 \cdot |x_0-x_2| \cdot a_2 = 2 \cdot |2-1| \cdot 2 = 4 minutes walking to the second building;  x_3 = 3: Divan will spend 2 \cdot |x_0-x_3| \cdot a_3 = 2 \cdot |2-3| \cdot 3 = 6 minutes walking to the third building. In total, Divan will spend 4 + 4 + 6 = 14 minutes. It can be shown that it is impossible to arrange buildings so that the businessman spends less time.Among others, x = [1, 3, 2, 0], x = [-5, -3, -6, -4] are also correct answers for the first example.
4
3
1 2 3
5
3 8 10 6 1
5
1 1 1 1 1
1
0

14 2 4 1 3 78 1 -1 0 2 3 4 18 3 6 1 5 2 4 0 1 2
['constructive algorithms', 'sortings', '*1000']