The linearly elastic planar structure shown in the figure is acted upon by two vertical concentrated forces. The horizontal beams $UV$ and $WX$ are connected with the help of the vertical linear spring constant $k= 20 \; \text{kN/m}.$ The fixed supports are provided at $U$ and $X.$ It is given that flexural rigidity $EI = 10^{5} \; \text{kN-m}^{2}, P = 100 \; \text{kN},$ and $a = 5 \; \text{m}.$ Force $Q$ is applied at the center of beam $WX$ such that the force in the spring $VW$ becomes zero.
The magnitude of force $Q$ (in $\text{kN}$) is __________.(round off to the nearest integer)