Nuclei of radioactive element A are produced at rate ‘ $t^2$ ’at any time t. The element A has decay constant $\lambda$ . Let N be the number of nuclei of element A at any time t. At time  $t=t_0,\frac{dN}{dt}$  is minimum. Then the  number of nuclei of element A at time  $t=t_0$ , is $\frac{m{t}_0-\lambda {z_0}^n}{{\lambda }^2}$  then m + n is____