Given that the complex numbers x,y,zx,y,zx,y,z satisfy the equations
x^2 + y^2 + z^2 & = & 2 \\
x^3 + y^3 + z^3 & = & 3 \\
x^4 + y^4 + z^4 & = & 4 \\
Denote f f f as a minimum degree monic polynomial with real coefficients such that it has root x+y+zx+y+zx+y+z.
What is the value of f(1)f(1)f(1)?