UFO Rectangles

Yandex has a secret department that handles special orders from the governments of different countries. Recently it received a message from a small banana republic that is suffering from an alien invasion.

Crop circles are strange circular formations that sometimes appear in potato or wheat fields, and they may or may not be left by UFOs. In the banana republic, the aliens leave rectangles of flattened banana plants instead.

The photo is divided into cells, and each cell is either intact or flattened. The aliens draw a rectangle by flattening all cells on the frame of an $r \times c$ rectangle, where $r$ and $c$ are both at least $3$. The frames never share cells, and no two frames touch along two or more sides.

XXXXXXXXX       XXXXX....        XXXXXXXXXX
X.XXXXX.X       X...XXXX.        X..XXXXX.X
X.X...X.X       X...XX.X.        X..X...X.X
X.XXXXX.X       X...XX.X.        X..X...X.X
X.......X       X...XXXX.        X..XXXXX.X
XXXXXXXXX       XXXXX....        XXXXXXXXXX

   OK              OK              NOT OK

Find all the rectangles the aliens drew so the department can investigate.

The first line contains two integers $n$ and $m$ ($3 \leq n, m \leq 2000$), the dimensions of the photo. Then $n$ lines follow, each with $m$ characters. Each character is . for an intact cell or X for a flattened cell.

It is guaranteed that the picture corresponds to some set of rectangles that satisfy the conditions above.

On the first line, print an integer $k$ ($k \geq 0$), the number of flattened rectangles in the photo. Then print $k$ lines, each with four integers $r_1$, $c_1$, $r_2$, and $c_2$ ($1 \leq r_1 < r_2 \leq n$, $1 \leq c_1 < c_2 \leq m$). These are the row and column numbers of the top-left and bottom-right corners of a rectangle. Rows are numbered 1 to $n$ from top to bottom, and columns are numbered 1 to $m$ from left to right.

Rectangles may be printed in any order. If several answers are possible, print any one of them.