Define a function F as follows
F(w,x,y,z)=81(S−T)
where
S=aw+bx+cy+dz−∣w−x∣−∣aw+bx−cy−∣w−x∣∣
T=∣aw+bx+cy−dz−∣w−x∣−∣aw+bx−cy−∣w−x∣∣∣
For certain positive integers a,b,c,d and for all w,x,y,z, this function F(w,x,y,z) always returns the lowest of the values w,x,y,z. For example
F(4,−3,2,1)=−3.
Let a,b,c,d be integer digits of a 4 digit integer A=abcd. What is the value of A?