B"Polycarp has n friends, the i -th of his friends has a_i candies. Polycarp's friends do not like when they have different numbers of candies. In other words they want all a_i to be the same. To solve this, Polycarp performs the following set of actions exactly once: Note that the number k is not fixed in advance and can be arbitrary. Your task is to find the minimum value of k . For example, if n=4 and a=[4, 5, 2, 5] , then Polycarp could make the following distribution of the candies: Note that in this example Polycarp cannot choose k=1 friend so that he can redistribute candies so that in the end all a_i are equal. For the data n and a , determine the minimum value k . With this value k , Polycarp should be able to select k friends and redistribute their candies so that everyone will end up with the same number of candies. The first line contains one integer t ( 1 <= t <= 10^4 ). Then t test cases follow. The first line of each test case contains one integer n ( 1 <= n <= 2 cdot 10^5 ). The second line contains n integers a_1, a_2, ldots, a_n ( 0 <= a_i <= 10^4 ). It is guaranteed that the sum of n over all test cases does not exceed 2 cdot 10^5 . For each test case output: "...