Question 127
Let $a, b, c, d$ be natural numbers such that $a + b + c + d = 2018$. Find the minimum value of the expression:
$$
E = (a - b)^2 + 2(a - c)^2 + 3(a - d)^2 + 4(b - c)^2 + 5(b - d)^2 + 6(c - d)^2.
$$
$$
E = (a - b)^2 + 2(a - c)^2 + 3(a - d)^2 + 4(b - c)^2 + 5(b - d)^2 + 6(c - d)^2.
$$