\begin{document}$V_{\rm NP}$\end{document}) that exhibit systematic differences among particle-particle, hole-hole, hole-particle, and particle-hole cases. A simple formula of \begin{document}$V_{\rm NP}$\end{document} is proposed to be in approximate linearity with \begin{document}$N_{n} N_{p}$\end{document}. This formula yields regular patterns of \begin{document}$ V_{\rm NP} $\end{document} that are highly consistent with those previously extracted according to binding energies. The observed ordering of \begin{document}$ V_{\rm NP} $\end{document}, i.e., \begin{document}$ V_{\rm NP} $\end{document} of the particle-particle case is the largest, \begin{document}$ V_{\rm NP} $\end{document} of the hole-hole case is in-between, and \begin{document}$ V_{\rm NP} $\end{document} of the particle-hole and hole-particle cases is the smallest, is explained in terms of the dominant part of \begin{document}$ V_{\rm NP} $\end{document} originating from symmetry energy and refinement involving the shell correction in the mass formulas."> Simple scenario of integrated neutron-proton interaction -
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