Let x_1, x_2, x_3, …, x_20 be in geometric progression with x_1=3 and the common ratio 1/2. A new data is constructed replacing each x_i by…

Let $\displaystyle x_1, x_2, x_3, \ldots, x_{20}$ be in geometric progression with $\displaystyle x_1=3$ and the common ratio $\displaystyle \frac{1}{2}$. A new data is constructed replacing each $\displaystyle x_i$ by $\displaystyle \left(x_i-i\right)^2$. If $\displaystyle \bar{x}$ is the mean of new data, then the greatest integer less than or equal to $\displaystyle \bar{x}$ is \_\_\_\_.