There is an $n \times n$ grid whose each square is empty or has a coin. On each move, you can remove all coins in a row or column.

What is the minimum number of moves after which the grid is empty?

Input

The first input line has an integer $n$: the size of the grid. The rows and columns are numbered $1,2,\dots,n$.

After this, there are $n$ lines describing the grid. Each line has $n$ characters: each character is either . (empty) or o (coin).

Output

First print an integer $k$: the minimum number of moves. After this, print $k$ lines describing the moves.

On each line, first print $1$ (row) or $2$ (column), and then the number of a row or column. You can print any valid solution.

Constraints

• $1 \le n \le 100$

Example

Input:

3
..o
o.o
...

Output:

2
1 2
2 3