Let  $f:ℝ\to ℝ$  be a function ,where $ℝ$  is the set of real numbers. The statements $S_1,S_2,S_3,S_4$   are given below, 
$S_1:$  If   $\left|f\left(x\right)-f\left(y\right)\right|\le 2024|x-y|$  for all $x,y$  then $f$  must be continuous everywhere.
$S_2:$  If  $\left|f\left(x\right)-f\left(y\right)\right|\le 2024|x-y|$  for all  $x,y$ then  $f$ must be differentiable everywhere.
$S_3:$  If  $\left|f\left(x\right)-f\left(y\right)\right|\le 2024{|x-y|}^2$ for all $x,y$  then $f$  must be differentiable everywhere.
$S_4:$  If $\left|f\left(x\right)-f\left(y\right)\right|\le 2024{|x-y|}^2$  for all $x,y$  then $f$  must be constant.
The number of statements among the  $S_1,S_2,S_3,S_4$  which are always true for every function