Functions $f,g$ and $h$ are defined by :

1. $f(x)=x+2$
2. $g(0)=f(1)$
3. $g(x)=f(g(x-1))$ , for $x \ge 1$
4. $h(0)=g(1)$
5. $h(x=g(h(x-1)))$ , for $x \ge 1$

Find $h(4)$。

A. $61$

B. $117$

C. $123$

D. $125$

E. $313$