Let $x_i\in\{+1,\ -1\}$, $i=1,\ 2,\ \cdots,\ 2n$. If their sum equals $0$ and the following inequality holds for any positive integer $k$ satisfying $1\le k < 2n$: $$x_1+x_2+\cdots + x_k\ge 0$$

Find the number of possible ordered sequence $\{x_1,\ x_2,\ \cdots,\ x_{2n}\}$.