**Time limit:**1.00 s**Memory limit:**512 MB

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