已知向量 $\alpha_1=\left(\begin{array}{l}1 \\ 0 \\ 1 \\ 1\end{array}\right), \alpha_2=\left(\begin{array}{c}-1 \\ -1 \\ 0 \\ 1\end{array}\right), \alpha_3=\left(\begin{array}{c}0 \\ 1 \\ -1 \\ 1\end{array}\right), \beta=\left(\begin{array}{c}1 \\ 1 \\ 1 \\ 1\end{array}\right)$, $\gamma=k_1 \alpha_1+k_2 \alpha_2+k_3 \alpha_3$. 若 $\gamma^T \alpha_1=\beta^T \alpha_i(i=1,2,3)$ ，则 $k_1^2+k_2^2+k_3^2=$