Determine all quadruplets (P,Q,R,S) of real numbers that satisfy this system of equations:

(Q+R+S)²⁰¹⁶ = 3P, and:

(P+R+S)²⁰¹⁶ = 3Q, and:

(P+Q+S)²⁰¹⁶ = 3R, and:

(P+Q+R)²⁰¹⁶ = 3S