Byteasar is visiting a carpet store looking at a certain carpet. Unfortunately, some fragments of the carpet are looking unsightly, due to factory defects. Because Byteasar would like to buy a substantial amount of the floor covering, he decided to allow himself to buy carpet with no more than one faulty spot. He will cover such a defect with a large flower-pot and the problem would be gone.

For simplicity, the carpet available in the store is represented as a rectangle with a height of $h$ and width $w$, divided into $h \times w$ squares of size $1 \times 1$. We know whether each carpet square has a defect, or not. Byteasar would like to buy a rectangular carpet piece which is as large as possible, consisting of square units, wherein at most one square is faulty. What is the area of such a piece?

Input

The first line of input contains two integers $h$ and $w$ ($1\leq h, w \leq 2000$), denoting respectively the height and width of the carpet available in the store.

Subsequent $h$ rows describe the carpet.

Each of these lines contains a string of $w$ characters . (square without faults), and # (faulty square), describing the individual carpet squares.

Output

Output the maximum area of a rectangular piece of the carpet, which consists of unit squares and has one defective square at most.

Examples

Input

4 5
#.#..
....#
..#..
....#

Output

12