Mike told Mat to consider three equations in three unknowns of the form a_ix + b_iy + c_iz = d_i (i = 1,2,3), where the coefficients and constants terms are consecutive factorials of integers. In other words, a_{1 =} n ! , b₁ = (n + 1) !, c₁ = (n + 2) !, d₁ = (n + 3) !, a₂ = (n + 4) !, etc. Find all values of n for which x + Y + z = 1500.