For any multiset $x_1,x_2,\ldots,x_{2n}$ of positive real numbers, a partition into two nonempty subsets $(A,B)$ is called "balanced" if $\text{sum}(A)\geq\text{sum}(B)-\max(B)$ and $\text{sum}(B)\geq\text{sum}(A)-\max(A)$.

What is the minimum number of balanced partitions, in terms of $n$?

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