K. Secret Level
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Petya loves playing computer games. He is currently playing yet another game and has just discovered a door to a secret level.

Next to the door, there is a square grid of size $$$n$$$ x $$$n$$$ cells. Some cells are black, and the others are white. If he clicks on any cell, its color will change to the opposite (black to white and white to black). At the same time, the colors of all neighboring (adjacent on the side) cells will also change. The door will open if all cells become the same color.

Help Petya open the door by making the minimum number of clicks.

Input

The first line of input contains an integer $$$n$$$ ($$$2 \le n \le 20$$$). The following $$$n$$$ lines contain $$$n$$$ characters each, either 'b' or 'w', where 'b' represents black color and 'w' represents white.

Output

If a solution exists, first output an integer $$$m$$$ — the minimum number of clicks. In each of the following $$$m$$$ lines, output the coordinates of the cell to be clicked — a pair of integers $$$y_i$$$ and $$$x_i$$$, where $$$y_i$$$ is the row number and $$$x_i$$$ is the column number. Rows are numbered from top to bottom, columns from left to right, numbering starts from one. If there are multiple correct answers, output any.

If there is no solution, output a single number -1.

Examples
Input
2
wb
bw
Output
2
1 2
2 1
Input
3
bbb
bbb
bbb
Output
0
Input
4
bbbb
wwwb
bbbb
bwww
Output
-1
Note

Illustration for the first example: