Algebra Level 5

$\displaystyle \sum_{k=1}^{n} |x_{k}|=19+\left|\sum_{k=1}^{n} x_{k}\right|\,.$

If $$x_i$$ is real,$$i\in\mathbb{N}$$,such that $$|x_{i}|<1$$.

What is the smallest possible value of $$n$$ such that it satisfy the equation above?

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