# The Mountain Song

Calculus Level pending

In a 2D Cartesian plane world, our friend Calvin wants to climb a mountain that is similar to the function $$f(x) = \displaystyle \sqrt[85]{{e}^{x}}$$. He starts at the point $$(0,1)$$.

Although 2D-Calvin is a skilled mountain climber, he cannot climb surfaces that have an inclination greater than $$85^{\circ}$$, and finishes his climbing by the point $$(x_0 , y_0)$$.

Catching a break so he can go back down, Calvin evaluates, to the nearest integer, his distance $$D$$ in meters to the starting point. Find $$D+1$$.

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