3. Let $a_{1}, a_{2}, \cdots, a_{m}$ be $m$ non-negative integers. Prove:
$$\begin{aligned} \min \left(a_{1}, a_{2}, \cdots, a_{m}\right)= & \sum_{1 \leqslant i_{1} \leqslant m} a_{i_{1}}-\sum_{1 \leqslant i_{1}<i_{2} \leqslant m} \max \left(a_{i_{1}}, a_{i_{2}}\right)+\cdots \\ & +(-1)^{k-1} \sum_{1 \leqslant i_{1}<\cdots<i_{k} \leqslant m} \max \left(a_{i_{1}}, \cdots, a_{i_{k}}\right) \\ & +\cdots+(-1)^{m-1} \max \left(a_{1}, \cdots, a_{m}\right) \end{aligned}$$