How to find the symmetric kernel for the given U-statistic?

The U-statistic is given by $$$$\widehat{\Delta}=\frac{1}{\binom{n_1}{2}\binom{n_2}{2}}\sum_{1\leq i_1 where \begin{align*} f(X_1,X_2,Y_1,Y_2)&=\min(Y_1,\max(X_1,X_2))-\min(X_1,X_2)I(\min(X_1,X_2)>Y_1) \\&-2X_1I(Y_1X_1). \end{align*} Since $$f(X_1,X_2,Y_1,Y_2)\neq f(X_2,X_1,Y_1,Y_2)$$ and $$f(X_1,X_2,Y_1,Y_2)\neq f(X_1,X_2,Y_2,Y_1)$$, $$f$$ is not symmetric in $$X$$ and $$Y$$. I have to find a symmetric kernel for the given U- statistic. I think \begin{align*} h(X_1,X_2,Y_1,Y_2)&=\frac{1}{4}\big[f(X_1,X_2,Y_1,Y_2)+f(X_2,X_1,Y_1,Y_2) \\&+f(X_1,X_2,Y_2,Y_1)+f(X_2,X_1,Y_2,Y_1)] \end{align*} is a symmetric kernel for the given u-statistic. Is this right? If my answer is wrong please let me know what the correct way is. Somebody please help me.