A group of total $16$ piles are arranged in a square grid format. The center-to-center spacing $(s)$ between adjacent piles is $3 \; \text{m}.$ The diameter $(d)$ and length of embedment of each pile are $1 \; \text{m}$ and $20 \; \text{m},$ respectively. The design capacity of each pile is $1000 \; \text{kN}$ in the vertical downward direction. The pile group efficiency $(\eta_{g})$ is given by
$$\eta_{g} = 1-\frac{\theta}{90} \left[\frac{(n-1)m + (m-1)n}{mn} \right]$$
where $m$ and $n$ are the number of rows and columns in the plan grid of the pile arrangement, and $\theta = \tan^{-1} \left(\dfrac{d}{s} \right).$
The design value of the pile group capacity (in $\text{kN}$) in the vertical downward direction is _______. (round off to the nearest integer)