You are given an binary matrix $A$ of $n$ rows and $m$ columns. In a move, from one cell, you can go to any of 4 adjacent cells (i.e. share the same edge). You cannot move to cell with number $1$.
Find the shortest distance from $(1, 1)$ to $(n, m)$.
### Input
- The first line contains 2 integers $n, m$.
- The next $n$ lines, each line contains a binary string of length $m$, matrix $A$.
### Output
- Print the distance from $(1, 1)$ to $(n, m)$, or print `-1` if no path exists.
### Constraints
- $1 \le n, m \le 10^3$.
### Example
Input:
```
4 5
01000
01010
00010
11010
```
Output:
```
11
```
