B'The company "Divan 's Sofas" is planning to build n + 1 different buildings on a coordinate line so that: 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. Each test contains several test cases. The first line contains one integer number t ( 1 <= t <= 10^3 ) -- the number of test cases. The first line of each case contains an integer n ( 1 <= n <= 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 <= a_i <= 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 . For 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 <= x_i <= 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. Let 's look at the first example. Divan will visit the first building a_1 = 1 times, the second a_2 = 2 times and th'...