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Using the exact representation of Carnot-Carathéodory balls in the Heisenberg group, we prove that: 1. $\left|{\nabla }_{{\mathbb{H}}^n}d\left(z,t\right)\right|=1$ in the classical sense for all $\left(z,t\right)\in {\mathbb{H}}^n$ with $z\ne 0$, where $d$ is the distance from the origin; 2. Metric balls are not optimal isoperimetric sets in the Heisenberg group.