Let  $S_1:$ If a function is not monotonic, then it does not have an inverse function.
$S_2:$  If a function is not monotonic on $(a,b),$ then its square cannot be monotonic on  $(a,b).$
$S_3:$  If both functions  $f\left(x\right)$ and $g\left(x\right)$  are continuous and monotonic on  $ℝ$, then their sum  $f\left(x\right)+g\left(x\right)$ is also monotonic or constant on  $ℝ.$
The number of statements among the  $S_1,S_2,S_3$ which are always true for every function