Two discrete-time signals $x[n]$ and $h[n]$ are both non-zero only for $n=0,1,2$, and are zero otherwise .It is given that

$$x[0]=1, \: x[1]=2, \: x[2]=1, \: h[0]=1$$ Let $y[n]$ be the linear convolution of $x[n]$ and $h[n]$. Given that $y[1]=3$ and $y[2]=4$, the value of the expression $(10y[3]+y[4])$ is__________.