Suppose that \left|x_{i}\right|<1 for i=1,2, \ldots, n. Suppose further that

\left|x_{1}\right|+\left|x_{2}\right|+\ldots+\left|x_{n}\right|=19+\left|x_{1}+x_{2}+\ldots+x_{n}\right| .

What is the smallest possible value of n ?

Suppose that \left|x_{i}\right|<1 for i=1,2, \ldots, n. Suppose further that

\left|x_{1}\right|+\left|x_{2}\right|+\ldots+\left|x_{n}\right|=19+\left|x_{1}+x_{2}+\ldots+x_{n}\right| .

What is the smallest possible value of n ?