A kid draws a series of triangles as shown in the figure above. The first triangle he draws has legs 1 and 1. All the triangles that he draws are right angled with base 1.

The last triangle that he can draw without overlapping the first one is the \(n^\text{th}\) triangle.

Then he overlaps the first triangle and continues drawing.

The last triangle he can draw without overlapping the first one again, is the \(m^\text{th}\) triangle.

Find \(n+m\).

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