+1341 Points $A,$ $B,$ and $C$ are given in the coordinate plane. There exists a point $Q$ and a constant $k$ such that for any point $P$,
\[PA^2 + PB^2 + PC^2 = 3PQ^2 + k.\]
If $A = (0,0),$ $B = (1,0),$ and $C = (-1,0)$, then find the constant $k$.
