Coin Grid

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