Friends and Candies

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:

• 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.