FourElements
\(A(x)=\sum x^{a_i}=\frac{x^{l_i}-x^{r_i+1}}{1-x}\)
\[F=\frac{1}{24}(\\
A(x)^4-\\
6\cdot A(x)^2A(x^2)+\\
3\cdot A(x^2)^2+\\
8\cdot A(x^3)A(x)-\\
6A(x^4)
\\)
\]
\[Answer=[x^s] F
\]
\[[x^t][(\frac{1}{1-x})^z]={t+z-1\choose z-1},z\geq 1,t\geq 0
\]
\(B(x)=A(x)^2(1-x)^2\)
\[A(x)^4=\sum_{\alpha+\beta\leq s} [[x^\alpha]B(x)]\cdot[[x^\beta]B(x)]{s-\alpha-\beta+3\choose 3}\\
{s-\alpha-\beta+3\choose 3}=(s-\alpha-\beta+3)*(s-\alpha-\beta+2)*(s-\alpha-\beta+1)\div6\\
=\sum coef_{i,j}\alpha^i\beta^j[[x^\alpha]B(x)]\cdot[[x^\beta]B(x)]\\
=\sum coef_{i,j}sum[i]\cdot sum[j]
\]
