The base of the right prism $A B C D A_{1} B_{1} C_{1} D_{1}$ is an isosceles trapezoid $A B C D$, where $B C \| A D, B C=5$, $A D=10, \angle B A D=\operatorname{arctg} 2$. A plane, perpendicular to the line $A_{1} D$, intersects the edges $A D$ and $A_{1} D_{1}$ at points $M$ and $N$ respectively, and $M D=A_{1} N=1$. Find the perimeter of the section of the prism by this plane.
31; cross-section - hexagon.

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