**Rule 86: If it exists, it can run Bad Apple!**
For the Gensokyo's light festival, Reimu prepared a $n \times n$ table of lanterns (a square of $n$ rows and $n$ columns) to play Bad Apple! As we know, a video consists of many frames. The current frame is $A$ and the next frame is $B$.
In one second, Reimu can flip the state of an entire row or an entire column of lanterns. Normally, transforming two frames shouldn't take longer than a split second, but we can wait.
Calculate the smallest time, in seconds, needed for Reimu to transform frame $A$ into frame $B$, or determine if it would take forever.
### Input
- The first line contains an integer $n$.
- The next $n$ lines each contain a binary string of length $n$, representing frame $A$, where `1` means the lantern is on and `0` means it's off.
- The following $n$ lines each contain a binary string of length $n$, representing frame $B$, with the same meaning.
### Output
- Print the minimum time, in seconds, required to transform $A$ into $B$. If time would end before Reimu could do so, print `-1`.
### Constraints
- $1 \le n \le 500$.
### Example
Input:
```
3
010
001
110
111
100
000
```
Output:
```
-1
```
