12. In an $n \times n$ matrix $\left( \begin{array} { c c c c c c c } 1 & 2 & 3 & \cdots & n - 2 & n - 1 & n \\ 2 & 3 & 4 & \cdots & n - 1 & n & 1 \\ 3 & 4 & 5 & \cdots & n & 1 & 2 \\ \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \\ n & 1 & 2 & \cdots & n - 3 & n - 2 & n - 1 \end{array} \right)$ , [Figure] Let the number in the $i$-th row and $j$-th column be denoted as $a _ { i j } ( i , j = 1,2 , \cdots , n )$ . When $n = 9$ , $a _ { 11 } + a _ { 22 } + a _ { 33 } + \cdots + a _ { 99 } =$ $\_\_\_\_$.
(5 points) Given the function $f ( x ) = \left\{ \begin{array} { l } | \lg x | , 0 < x \leqslant 10 \\ - \frac { 1 } { 2 } x + 6 , x > 10 \end{array} \right.$, if $a , b , c$ are mutually distinct and $f ( a ) = f ( b ) = f ( c )$, then the range of $abc$ is
12. In an $n \times n$ matrix $\left( \begin{array} { c c c c c c c } 1 & 2 & 3 & \cdots & n - 2 & n - 1 & n \\ 2 & 3 & 4 & \cdots & n - 1 & n & 1 \\ 3 & 4 & 5 & \cdots & n & 1 & 2 \\ \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \\ n & 1 & 2 & \cdots & n - 3 & n - 2 & n - 1 \end{array} \right)$ ,\\
\includegraphics[max width=\textwidth, alt={}, center]{1a5db6ae-0a01-48d9-8bc5-a5e1048171b6-01_1022_428_1169_1425}
Let the number in the $i$-th row and $j$-th column be denoted as $a _ { i j } ( i , j = 1,2 , \cdots , n )$ .\\
When $n = 9$ , $a _ { 11 } + a _ { 22 } + a _ { 33 } + \cdots + a _ { 99 } =$ $\_\_\_\_$.