Let $I_{3}$ be an inverse semigroup consisting of all partial bijections on a set $\{1,2,3\}$, called the symmetric inverse semigroup. Then \begin{align*} I_{3}=\left\{\emptyset, \binom{1}{1}，\binom{1}{2}，\binom{1}{3}，\binom{2}{1}，\binom{2}{2}，\binom{2}{3}，\binom{3}{1}，\binom{3}{2}，\binom{3}{3}，\binom{1,2}{1,2}，\\ \binom{1,2}{1,3}， \binom{1,2}{2,3}，\binom{1,2}{2,1}，\binom{1,2}{3,1}，\binom{1,2}{3,2}，\binom{1,3}{1,2}, \binom{1,3}{1,3}, \binom{1,3}{2,3}, \binom{1,3}{2,1}, \binom{1,3}{3,1},\\ \binom{1,3}{3,2}, \binom{2,3}{2,3}, \binom{2,3}{2,1}, \binom{2,3}{3,1}, \binom{2,3}{3,2}, \binom{2,3}{1,2}, \binom{2,3}{1,3}, \binom{1,2,3}{1,2,3}, \binom{1,2,3}{1,3,2}, \\ \binom{1,2,3}{2,3,1}, \binom{1,2,3}{2,1,3}, \binom{1,2,3}{3,2,1}, \binom{1,2,3}{3,2,1}\right\}. \end{align*}
I want to find all generators and relations of $I_{3}$. Can someone help me? Thanks in advance.