A lake can be represented by a matrix $A$ of size $n \times m$:
- `X` represents an iceberg.
- `.` represents a normal area.
After a day, icebergs that are adjacent to water will melt. For example:
```
..... .....
..X.. .....
.XXX. --- After a day ---> ..X..
.XX.. .....
XXX.. .X...
```
From a cell you can move to any of the 4 adjacent cells as long as it is not an iceberg. There are exact two points denoted by letter `L`. Determine after how many days two points are connected.
### Input
- The first line contains 2 integers $n,m$.
- The next $n$ lines, each line contains a string of $m$ character. There are exactly 2 characters `L`.
### Output
- Print the number of days after which two points are connected.
### Constraints
- $1 \le n,m \le 1500$.
### Example
Input:
```
5 5
L....
XXXXX
XXXXX
XXXXX
....L
```
Output:
```
2
```
