Bounded complete weakly nonregular surfaces with negative curvature bounded away from zero

In three-dimensional Euclidean space we construct a bounded saddle surface of class $C^1$, complete in its intrinsic metric. This surface has $C^\infty$ regularity everywhere except for a countable set of singular points (saddle points of the third order, isolated in the intrinsic metric). The Gaussian curvature in the sense of A. D. Aleksandrov is defined on the whole surface, is continuous and differentiable, and satisfies the inequality $K\leqslant-1$.
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