B. Friends and Candiestime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputPolycarp 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:   Polycarp chooses k (0 \le k \le n) arbitrary friends (let's say he chooses friends with indices i_1, i_2, \ldots, i_k);  Polycarp distributes their a_{i_1} + a_{i_2} + \ldots + a_{i_k} candies among all n friends. During distribution for each of a_{i_1} + a_{i_2} + \ldots + a_{i_k} candies he chooses new owner. That can be any of n friends. Note, that any candy can be given to the person, who has owned that candy before the distribution process. 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:   Polycarp chooses k=2 friends with indices i=[2, 4] and distributes a_2 + a_4 = 10 candies to make a=[4, 4, 4, 4] (two candies go to person 3). 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.InputThe first line contains one integer t (1 \le t \le 10^4). Then t test cases follow.The first line of each test case contains one integer n (1 \le n \le 2 \cdot 10^5).The second line contains n integers a_1, a_2, \ldots, a_n (0 \le a_i \le 10^4).It is guaranteed that the sum of n over all test cases does not exceed 2 \cdot 10^5.OutputFor each test case output:   the minimum value of k, such that Polycarp can choose exactly k friends so that he can redistribute the candies in the desired way;  "-1" if no such value k exists. ExampleInput
5
4
4 5 2 5
2
0 4
5
10 8 5 1 4
1
10000
7
1 1 1 1 1 1 1
Output
2
1
-1
0
0

5
4
4 5 2 5
2
0 4
5
10 8 5 1 4
1
10000
7
1 1 1 1 1 1 1

2 1 -1 0 0 
['greedy', 'math', '*800']