current item	input history	f output	$\overline{f}$ output
	ε	ε	ε
3	3	3	3
1	3 1	ε	3
5	3 1 5	5	3 5
2	3 1 5 2	ε	3 5

Notice that $\overline{f}(3152)=f(\epsilon )\cdot f(3)\cdot f(31)\cdot f(315)\cdot f(3152)$.