Block A of mass $m$ and block $B$ of mass $2m$ are placed on a fixed tringular wedge by means of a massless inextensible string and a frictionless pulley as shown in figure . The wedge is inclined at ${45}^{\circ }$ to the horizointal on both sides. If the coefficient of friction between the block $A$ and the wedge is $\frac{2}{3}$ and that between block B and the wedge is $\frac{1}{3}$ and both the blocks $A$ and $B$ are released from rest, the acceleration of $A$ will be