Given  $a,b\in \{0,1,2,3,\mathrm{......},19,20\}$, consider the system of equations
x + y + z = 4
2x + y + 3z = 6
x + 2y + az = b
Let
P denotes number of order pairs (a, b) so that system of equations has a unique solution.
Q denotes number of ordered pairs (a, b) so that system of equations has no solution.
R denotes number of ordered pairs (a, b) so that system of equations has infinite solutions, then $(P + Q + R)$ is: