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:

• Increase length of one stick by 1.
• Reduce the length of one stick. If the stick has length L, the new length will be \(\lfloor {L \over 2} \rfloor\).

Your task is to help Kevin and say the minimum number of seconds to make all sticks have equal length.

Input format:

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 a_i.

Output format:

For every test case output the minimum number of seconds Kevin need to achieve his goal.

Constraints:

• \(1 \le t \le 10\)
• \(1 \le n \le 1000, 1 \le a_i \le 1000\) in 20% of the test cases.
• \(1 \le n \le 1000, 1 \le a_i \le 10^9\) in 40% of the test cases.
• \(1 \le n \le 10^5, 1 \le a_i \le 10^9\) in 40% of the test cases.