Decomposing a mixed distribution function into its discrete and continuous parts

Suppose a distribution function $F:\mathbb{R}\to[0,1]$ is as follows: $F(x)=0$ for $x<0$; $1/4$ for $0\le x<1$; $1/2$ for $1\le x<2$; $1/2+(x-2)/2$ for $2\le x<3$; $1$ for $x\ge3$. Then $F(x)=l_1F_1(x)+l_2F_2(x)$ where: