You are given an integer array $A$ consisting of $N$ elements. You can perform the following operations on array $A$:

• Choose any element and increase or decrease it by 3 for 1 coin.
• Choose any element and increase or decrease it by 2 for free.

You are required to spend the minimum number of coins in order to make all the elements in array $A$ equal.

Input format

• The first line contains an integer $T$ denoting the number of test cases. 
• The first line of each test case contains an integer $N$ denoting the number of elements in array $A$.
• The second line of each test case contains $N$ space-separated integers of array $A$.

Output format

Print $T$ lines. For each test case, print a single line denoting the minimum number of coins to make all elements equal.

Constraints

$1 \leq T \leq 20000$

$1 \leq N \leq 100000$

$1 \leq A_i \leq 10^9 \forall i \in [1,N]$

Sum of $N$ over all test cases does not exceed 500000