Luke is daydreaming in Math class. He has a sheet of graph paper with $n$ rows and $m$ columns, and he imagines that there is an army base in each cell for a total of $n\cdot m$ bases. He wants to drop supplies at strategic points on the sheet, marking each drop point with a red dot. If a base contains at least one package inside or on top of its border fence, then it's considered to be supplied. For example:

Given $n$ and $m$, what's the minimum number of packages that Luke must drop to supply all of his bases?

Example

$n=2$

$m=3$

Packages can be dropped at the corner between cells (0, 0), (0, 1), (1, 0) and (1, 1) to supply ${4}$ bases. Another package can be dropped at a border between (0, 2) and (1, 2). This supplies all bases using $2$ packages.

Function Description

Complete the gameWithCells function in the editor below.

gameWithCells has the following parameters:

int n: the number of rows in the game
int m: the number of columns in the game

Returns

int: the minimum number of packages required

Input Format

Two space-separated integers describing the respective values of $n$ and $m$.

Constraints

$0<n,m\leq1000$

Sample Input 0
2 2

Sample Output 0
1

Explanation 0

Luke has four bases in a $2\times2$ grid. If he drops a single package where the walls of all four bases intersect, then those four cells can access the package:

Because he managed to supply all four bases with a single supply drop, we print ${1}$ as our answer.

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