# Huffman Merge Cost

## Description

Repeatedly merge two available weights, paying their sum each time, until one weight remains. Find the minimum possible total cost.

## Input

The function receives the input weights and a writable work array.

## Output

Return the minimum total merge cost.

## Constraints

- $1 \le n \le 8$.
- $1 \le weight_i \le 1000$.

## Source

Classical Huffman optimal-merge problem reconstructed from the verified C artifact.