3. Let $1997=2^{a_{1}}+2^{a_{2}}+\cdots+2^{a_{n}}$, where $a_{1}, a_{2}, \cdots, a_{n}$ are distinct non-negative integers, calculate the value of $a_{1}+a_{2}+\cdots+a_{n}$.
3. According to the knowledge in Example 1, 1997 can be uniquely expressed as $1997=2^{10}+2^{9}+2^{8}+2^{7}+2^{6}+2^{3}+2^{2}+2^{0}$, so the required sum is 45.