Consider the sequence: \(x_{n+1} = 4x_n(1 âˆ’ x_n)\)

Call a point \(x_0\in[0, 1]\) is \(râˆ’\)periodic if \(x_r=x_0\). For example, \(x_0 = 0\) is always a \(râˆ’\)periodic fixed point for any \(r\).

Let \(N\) be the number of positive \(2015âˆ’\)periodic fixed points.

Find the last 3 digits of \(N\).

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