Let N be the set of positive integers. Find all functions f:N->N that satisfy the equation

f^{abc-a}(abc) + f^{abc-b}(abc) + f^{abc-c}(abc) = a + b + c

for all a, b, c ≥ 2.

(Here f^{1}(n) = f(n) and f^{k}(n) = f(f^{k-1}(n)) for every integer k greater than 1)
(Also note: abc is the product a·b·c and not the concatenation 100a+10b+c)