If $\mathbf{x}^{\mathbf{2}} + \mathbf{x} + \mathbf{1} = \mathbf{0}$,
then $\left(x + \frac{1}{x}\right)^{4} + \left(x^{2} + \frac{1}{x^{2}}\right)^{4} + \left(x^{3} + \frac{1}{x^{3}}\right)^{4} + \cdots + \left(x^{25} + \frac{1}{x^{25}}\right)^{4}$ is