Find the number of functions f from \{0,1,2,3,4,5,6\} to the integers such that f(0)=0, f(6)=12, and

|x-y| \leq|f(x)-f(y)| \leq 3|x-y|

for all x and y in \{0,1,2,3,4,5,6\}.

Find the number of functions f from \{0,1,2,3,4,5,6\} to the integers such that f(0)=0, f(6)=12, and

|x-y| \leq|f(x)-f(y)| \leq 3|x-y|

for all x and y in \{0,1,2,3,4,5,6\}.