At KSA, the morning roll call is conducted in the cafeteria in the form of an attendance check. There are a total of $N \cdot M$ students at KSA, and each student is assigned a distinct number from $1$ to $N \cdot M$. The attendance sheet is arranged in $N$ rows and $M$ columns, with students' numbers written in the cells. Each student finds their own number and draws a circle on it to indicate participation in the morning roll call. In the cell of the $i$-th row and $j$-th column, the number $i + N(j-1)$ is written. Each number can be circled at most once.

However, some lazy students have started asking their friends to attend roll call for them. A student who attends roll call for someone else quickly draws two circles around their number and the other student's number while the dorm supervisor is not watching. To avoid being caught, a student can only attend for another student if their numbers differ by exactly $1$ and their cells on the attendance sheet share a side.

Given the current attendance status of the students, determine the minimum number of additional students who must come so that attendance for all students can be completed.

Input

The first line contains two space-separated integers $N$ and $M$.

The $i$-th line of the following $N$ lines contains a string $S_i$. Each $S_i$ is a string of length $M$ consisting only of characters O and X.

If the $j$-th character of $S_i$ is O, then student number $i+N(j-1)$ has already completed the morning roll call. If it is X, then student number $i+N(j-1)$ has not yet completed the morning roll call.

Output

On the first line, print $k$, the minimum number of students who must come to the cafeteria so that every student's roll call can be completed.

Print one of the following on each of the next $k$ lines. If the student only completes their own roll call, print $1$ and their number, separated by a space. If the student attends roll call for someone else, print $2$ and the two students' numbers, separated by spaces.

The order of the student numbers and the $k$ lines does not matter. If there are multiple solutions, print any of them.

Constraints

• $1 \le N, M \le 100$
• At least one of $S_i$ contains an X

Scoring

Examples

Input 1

3 2
XO
XX
XO

Output 1

3
1 3
2 1 2
1 5

Input 2

5 1
O
X
X
X
O

Output 2

2
1 2
2 4 3

Input 3

1 4
XXXX

Output 3

2
2 2 1
2 3 4