Two blocks A and B of masses m and 2m are placed on a smooth floor and are connected by a spring. A third block C of mass m moves with a velocity v₀ and collides head-on and elastically with A as shown. After some time, it is found that the instantaneous velocities of A and B are the same and the instantaneous compression of the spring is x₀. If spring constant of the spring is $\mathrm{k}=\frac{2{\mathrm{mv}}_0^2}{{\mathrm{nx}}_0^2}$, then the value of n is