Kevin has $$n$$ sticks. i-th stick has length $$a_i$$.
Kevin wants every stick has the same length. To achieve his goal he can perform one of the following operation in one second:
Your task is to help Kevin and say the minimum number of seconds to make all sticks have equal length.
The first line of input will contain an integer t, denoting the number of test cases.
Each test case starts with the integer n. The next line contains n space-separated integers ai.
For every test case output the minimum number of seconds Kevin need to achieve his goal.
Sequence of operations:
1) Break first stick. New length will be 3.
2) Increase length of the first stick. New length will be 4.
3) Increase length of the third stick. New length will be 4.
4) Break the last stick. New length will be 4.