<Tri-2025-2232>, hint

 Let AH be altitude of triangle ABC, H on BC.

Since ABH, ACH are right triangles and M,N are the midpoints of ABH, ACH

AM=BM=MH and AN=NC=NH. when S=H (MA-MS)(NB-NH)=0 and when S on BH

(MB-MS)>0, (NC-NS)<0 (MB-MS)(NC-NS)<0