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 \le n \le 1000$.
- $-10^9 \le x, y \le 10^9$.
### Example
Input:
```
3 0 0
2 0
0 2
2 2
```
Output:
```
1.4142
```
