Let $m_1, m_2$ be the slopes of two adjacent sides of a square of side $a$ such that $a^{2}+11a+3\left(m_{1}^{2}+m_{2}^{2}\right)=220.$ If one vertex of the square is $\big(10(\cos\alpha-\sin\alpha),\,10(\sin\alpha+\cos\alpha)\big)$, where $\alpha\in(0,\tfrac{\pi}{2})$, and the equation of one diagonal is $(\cos\alpha-\sin\alpha)x+(\sin\alpha+\cos\alpha)y=10$, then $ 72\left(\sin^{4}\alpha+\cos^{4}\alpha\right)+a^{2}-3a+13 $ is equal to: