A square is inscribed in the circle $x^2+y^2-10 x-6 y+30=0$. One side of this square is parallel to $y= x+3$. If $\left(x_i, y_i\right)$ are the vertices of the square, then $\sum\left(\mathrm{x}_{\mathrm{i}}^2+\mathrm{y}_{\mathrm{i}}^2\right)$ is equal to :
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