Putnam 1973

Let $ABC$ be any triangle. Let $X, Y, Z$ be points on the sides $BC, CA, AB$ respectively. Suppose the distances $BX \leq XC, CY \leq YA, AZ \leq ZB$. Given that the area of the triangle $XYZ$ is $\geq n$ (area of triangle $ABC$) find the lowest non-zero value of $n$.