We are playing a puzzle. An upright board with $H$ rows by $W$ columns of cells, is used in this puzzle.
A stone in $i$-th row and $j$-th column engraved with a digit, one of 1 through 9, is placed in each of the cells.
You can erase 1 cell in the board.
The game process is following:
When $K$ or more stones in horizontally adjacent cells are engraved with the same digit, the stones will disappear. Disappearances of all such groups of stones take place simultaneously.
When stones are in the cells above the emptied cells, these stones drop down so that the emptied cells are filled.
After the completion of all stone drops, if one or more groups of stones satisfy the disappearance condition, repeat by returning to the step 1.
Score is $\sum_i 2^i \times \left(\text{Sum of numbers in the stones which disappeared in the $i$-th chain (0-indexed)}\right)$.
Please answer the points if he erased the optimal place.
Input
The input is given from standard input in the following format.