Given a convex polygon of n vertices and a point A(x,y) locating outside of the polygon. Find the shortest distance from A to the polygon.
### Input
- The first lines contains three integer n,x,y.
- The next n lines, each line contains two integers x,y, which describes a vertex of the polygon. The points are listed in clockwise order.
### Output
- Print the shorest distance. Your answer will be considered correct if its absolute or relative error does not exceed 10−3. In other words, your answer, x, will be compared to the correct answer, y. If |x−y|<10−3, then your answer will be considered correct.
### Constraints
- 1≤n≤1000.
- −109≤x,y≤109.
### Example
Input:
300200222
Output:
1.4142
