Load Balancing

学校里有$n$个服务器，第$i$个服务器有$m_{i}$个任务。 你可以对服务器的任务分配做**多次调整**，每次可以将一个任务从一个服务器$a$调整到另一个服务器$b$，这会使$m_{a}$减小$1$、$m_{b}$增加$1$，并**耗费$1$秒的时间**。 请求出**最少多少秒**可以使任务分配得尽量平衡。 任务分配得尽量平衡指的是：任务最多的服务器与任务最少的服务器的任务数量的差距尽量小，简单说，就是最小化$m_{max}-m_{min}$ 。

In the school computer room there are $ n $ servers which are responsible for processing several computing tasks. You know the number of scheduled tasks for each server: there are $ m_{i} $ tasks assigned to the $ i $ -th server. In order to balance the load for each server, you want to reassign some tasks to make the difference between the most loaded server and the least loaded server as small as possible. In other words you want to minimize expression $ m_{a}-m_{b} $ , where $ a $ is the most loaded server and $ b $ is the least loaded one. In one second you can reassign a single task. Thus in one second you can choose any pair of servers and move a single task from one server to another. Write a program to find the minimum number of seconds needed to balance the load of servers.

The first line contains positive number $ n $ ( $ 1<=n<=10^{5} $ ) — the number of the servers. The second line contains the sequence of non-negative integers $ m_{1},m_{2},...,m_{n} $ ( $ 0<=m_{i}<=2·10^{4} $ ), where $ m_{i} $ is the number of tasks assigned to the $ i $ -th server.

Print the minimum number of seconds required to balance the load.

2
1 6

2

7
10 11 10 11 10 11 11

0

5
1 2 3 4 5

3

In the first example two seconds are needed. In each second, a single task from server #2 should be moved to server #1. After two seconds there should be 3 tasks on server #1 and 4 tasks on server #2. In the second example the load is already balanced. A possible sequence of task movements for the third example is: 1. move a task from server #4 to server #1 (the sequence $ m $ becomes: 2 2 3 3 5); 2. then move task from server #5 to server #1 (the sequence $ m $ becomes: 3 2 3 3 4); 3. then move task from server #5 to server #2 (the sequence $ m $ becomes: 3 3 3 3 3). The above sequence is one of several possible ways to balance the load of servers in three seconds.