You are given an integer array of length $3n$. You must remove exactly $n$ elements from the array, and the remaining $2n$ elements must be split into two parts of length $n$ each:

• the first $n$ kept elements from the left side,
• the last $n$ kept elements from the right side.

Your goal is to minimize the difference between the sum of the left kept part and the sum of the right kept part.

Return the minimum possible value of:

$\text{sum(left kept n elements)} - \text{sum(right kept n elements)}$

The removed elements can come from anywhere, but the kept left part must be chosen from a prefix and the kept right part must be chosen from a suffix in the natural order of the array.