The number of relations, on the set  $\{1,2,3\}$  containing (1,2) and (2,3), which are reflexive and transitive but not symmetric, is _____.

$$\begin{gathered} R_1=\left\{(1,1)(2,2)(3,3)(1,2)(2,3)(1,3)\right\} \\ {R}_2=\left\{(1,1)(2,2)(3,3)(1,2)(2,3)(1,3)(2,1)\right\} \\ {R}_3=\left\{(1,1)(2,2)(3,3)(1,2)(2,3)(1,3)(3,2)\right\} \\ The above three relations are reflexive, transitive but not symmetric \end{gathered}$$