OME 2002 Problem 3

The function $g$ is defined about the natural numbers and satisfies the following conditions: $g(2) = 1$ $g(2n) = g(n)$ $g(2n+1) = g(2n) +1.$ Where $n$ is a natural number such that $1 \leq n \leq 2002$ .

Find the maximum value $M$ of $g(n).$ Also, calculate how many values of $n$ satisfy the condition of $g(n) = M.$