Logic Level 2

Dan and Sam play a game on a convex polygon of 100001 sides. Each one draws a diagonal on the polygon in his turn.

When someone draws a diagonal, it cannot have common points (except the vertices of the polygon) with other diagonals already drawn.

The game finishes when someone can't draw a diagonal on the polygon following the rules; that person is the loser. If Dan begins, who will win? This means, who has a winning strategy?

Clarification: The diagonals of a polygon are straight lines that join non-adjacent vertices.

This is the fourteenth problem of the set Winning Strategies.

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