$P(x)=x^{100}+a_{99}x^{99}+a_{98}x^{98}+...+a_{2}x^2+a_{1}x+1$ is a polynomial function with all real and positive coefficients, that is, $a_{1},a_{2},...,a_{99} \in R^{+}$. It is known that all the roots of the equation $P(x)=0$ are real.

If $\displaystyle \sum_{i=1}^{99} a_{i} \geq 2(2^{N}-1)$ where $N$ is a positive integer, then find the maximum value of $N$.