A vector field

𝐁(𝑥, 𝑦, 𝑧) = 𝑥 𝑖̂+ 𝑦 ĵ− 2𝑧 k̂

is defined over a conical region having height ℎ = 2, base radius 𝑟 = 3 and axis along z, as shown in the figure. The base of the cone lies in the x-y plane and is centered at the origin.

If 𝒏 denotes the unit outward normal to the curved surface 𝑆 of the cone, the value of the integral

                               ∫_s𝐁 S ⋅ 𝒏 dS    equals _________ . (Answer in integer)