Let x2+y2+xy+1≥a(x+y)∀x,y∈R, then the number of possible integer(s) in the range of a is________.

x2+x(y−a)+y2−ay+1≥0x∈R ⇒    (y−a)2−4y2−ay+1≤0⇒    −3y2+2ay+a2−4≤0∴    3y2−2ay+4−a2≥0 y∈R    D≤0⇒    4a2−4,34−a2≤0⇒    a2−34−a2≤0⇒4a2−12≤0∴     Range of a∈(−3,3)⇒     number of integer {−1,0,1}