A function f is defined for all real numbers and satisfies
f(2+x)=f(2-x) \quad \text { and } \quad f(7+x)=f(7-x)
for all real x. If x=0 is a root of f(x)=0, what is the least number of roots f(x)=0 must have in the interval -1000 \leq x \leq 1000 ?