3. For a sequence of real numbers $x_{1}, x_{2}, \cdots, x_{n}$, define its "value" as $\max _{1 \leqslant i \leqslant n}\left\{\left|x_{1}+x_{2}+\cdots+x_{i}\right|\right\}$. Given $n$ real numbers, David and George want to arrange these $n$ numbers into a sequence with low value. On one hand, diligent David examines all possible ways to find the minimum possible value $D$. On the other hand, greedy George chooses $x_{1}$ such that $\left|x_{1}\right|$ is as small as possible. From the remaining numbers, he chooses $x_{2}$ such that $\left|x_{1}+x_{2}\right|$ is as small as possible, $\cdots \cdots$ At the $i$-th step, he chooses $x_{i}$ from the remaining numbers such that $\left|x_{1}+x_{2}+\cdots+x_{i}\right|$ is as small as possible. At each step, if there are multiple numbers that give the same minimum absolute sum, George arbitrarily chooses one. Finally, the value of the sequence he gets is $G$. Find the smallest constant $c$, such that for every positive integer $n$, every array of $n$ real numbers, and every sequence George can obtain, we have
$$
G \leqslant c D \text {. }
$$