Let S ={1,2,3,4}. Then the number of elements in the set {f: S × S → S: f is onto and f( a, b )=f( b, a ) ≥ a ∀( a, b ) ∈ S × S } is \ \ \ \.

Let $\displaystyle \mathrm{S}=\{1,2,3,4\}$. Then the number of elements in the set $\displaystyle \{f: \mathrm{S} \times \mathrm{S} \rightarrow \mathrm{S}: f$ is onto and $\displaystyle f(\mathrm{a}, \mathrm{b})=f(\mathrm{~b}, \mathrm{a}) \geqslant \mathrm{a} \forall(\mathrm{a}, \mathrm{b}) \in \mathrm{S} \times \mathrm{S}\}$ is \_\_\_\_.