INMO 1999 Problem 1

Let $ABC$ be an acute-angled triangle in which $D,E,F$ are points on $BC,CA,AB$ respectively such that $AD \perp BC$ ; $AE = BC$ ; and $CF$ bisects $\angle C$ internally, Suppose $CF$ meets $AD$ and $DE$ in $M$ and $N$ respectively. If $FM$ $= 2$ , $MN =1$ , $NC=3$ , find the perimeter of $\Delta ABC$ .