Let $F:M\to M$ is a smooth map where $M$ is compact connected smooth manifold and $F\circ F=F$ then show that $F(M)$ is a submanifold of $M$.

Question

Given here composition of $F$ with $F$ gives $F$ then to show $F(M)$ is a submanifold of $M$. I was thinking in the way that $F(M)$ should be inverse image of some regular value of some smooth function which needs to constructed using this property of $F$ but unable to proceed in this direction. Any hints regarding how to proceed?