Consider a positive integer $n=\overline{a_1a_2...a_k},k\ge 2$.A trunk of $n$ is a number of the form $\overline{a_1a_2...a_t},1\le t\le k-1$.(For example,the number $23$ is a trunk of $2351$.) By $T(n)$ we denote the sum of all trunk of $n$ and let $S(n)=a_1+a_2+...+a_k$.Prove that $n=S(n)+9\cdot T(n)$.