Marisa and Reimu have lost each other in the Bamboo Forest of the Lost. The forest can be represented as a undirected graph of n vertices and m edges. Marisa is currently at vertex a, and Reimu is currently at vertex b.
Every 1 unit of time, Marisa and Reimu move to any adjacent vertex (they will not stand still, as they are in a hurry now). Find the earliest time when they will meet each other again.
### Input
- The first line contains 2 integers n,m.
- The second line contains 2 integers a,b.
- The next m lines, each line contains 2 integers u,v, there is an edge between u and v.
### Output
- Print the earliest time when they will meet each other again. Or print −1 if they get lost forever...
### Constraints
- 1≤n,m≤105.
- 1≤u,v,a,b≤n.
### Example
Input:
6616122334246554
Output:
2
#### **Note**: Marisa and Reimu will meet each other at 4.