a!+b!+c!=a!⋅b!
If a,b,c are nonnegative integers, then there are a finite number of solutions to the above equation. Let them be (a1,b1,c1),(a2,b2,c2),(a3,b3,c3),…,(an,bn,cn) in some order. Find the value of
n+i=1∑n(ai+bi+ci).
(If n=0, then the sum is zero, so you should write 0 as the answer.)