A conducting resistance less rod is bent as parabola $y=K{x}^2,$ where ‘$K$’ is a constant. A horizontal conductor of resistance per unit length $\lambda$ starts sliding up on the parabola starting from x-axis with a constant acceleration a and the parabolic frame starting rotating with constant angular frequency $\omega$ about the axis of symmetry, both starting t = 0 as shown in the figure. There exist a uniform magnetic field B as shown in figure . The current induced in the rod when frame turns through an angle $\frac{\pi }{4}is\frac{Ba\pi (\pi -12)}{n\times 12\sqrt{2}\omega \lambda }\text{.}$  The value of ‘$n$’ is