To celebrate your birthday you have prepared a festive table! Now you want to seat as many guests as possible.

The table can be represented as a rectangle with height $h$ and width $w$, divided into $h \times w$ cells. Let $(i, j)$ denote the cell in the $i$-th row and the $j$-th column of the rectangle ($1 \le i \le h$; $1 \le j \le w$).

Into each cell of the table you can either put a plate or keep it empty.

As each guest has to be seated next to their plate, you can only put plates on the edge of the table — into the first or the last row of the rectangle, or into the first or the last column. Formally, for each cell $(i, j)$ you put a plate into, at least one of the following conditions must be satisfied: $i = 1$, $i = h$, $j = 1$, $j = w$.

To make the guests comfortable, no two plates must be put into cells that have a common side or corner. In other words, if cell $(i, j)$ contains a plate, you can't put plates into cells $(i - 1, j)$, $(i, j - 1)$, $(i + 1, j)$, $(i, j + 1)$, $(i - 1, j - 1)$, $(i - 1, j + 1)$, $(i + 1, j - 1)$, $(i + 1, j + 1)$.

Put as many plates on the table as possible without violating the rules above.