COMC 2016 B Problem 2

The squares of a 6 \times 6 square grid are each labeled with a point value. As shown in the diagram below, the point value of the square in row i and column j is i \times j.

\begin{array}{|c|c|c|c|c|c|} \hline 6 & 12 & 18 & 24 & 30 & 36 \\ \hline 5 & 10 & 15 & 20 & 25 & 30 \\ \hline 4 & 8 & 12 & 16 & 20 & 24 \\ \hline 3 & 6 & 9 & 12 & 15 & 18 \\ \hline 2 & 4 & 6 & 8 & 10 & 12 \\ \hline 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \end{array}

A path in the grid is a sequence of squares, such that consecutive squares share an edge and no square occurs twice in the sequence. The score of a path is the sum of the point values of all squares in the path.

Determine the highest possible score of a path that begins with the bottom left corner of the grid and ends with the top right corner.