The solution of an ordinary differential equation $y^{\prime \prime \prime}+3 y^{\prime \prime}+3 y^{\prime}+y=30 e^{-t}$ is
\[
y(t)=\left(c_{0}+c_{1} t-c_{2} t^{2}+c_{3} t^{3}\right) e^{-t}
\]
Given $y(0)=3, y^{\prime}(0)=-3$ and $y^{\prime \prime}(0)=-47$, the value of $\left(c_{0}+c_{1}+c_{2}+c_{3}\right)$ is (rounded off to nearest integer).
Note: $y^{\prime \prime \prime}=d^{3} y / d t^{3}, y^{\prime \prime}=d^{2} y / d t^{2}, y^{\prime}=d y / d t$ and $c_{0}, c_{1}, c_{2}, c_{3}$ are constants.