There are $n$ radars on a 2D plane. The $i^{th}$ is located at the point $(x_i, y_i)$.
All $n$ radars have the same trasmitting power $R$. Radar $A$ and radar $B$ can be connected directly if their distance does not exceed $2 \times R$, or they can be connected through another intermediate radar.
Find the minimum possible $R$ so that $n$ radars are connected.
### Input
- The first line contains an integer $n$.
- The next $n$ lines, each line contains 2 integers $(x_i, y_i)$.
### Output
- Print the minimum $R$, rounding **exactly** to 6 decimal places.
### Constraints
- $1 \le n \le 10^3$.
- $1 \le x_i, y_i \le 10^9$.
### Example
Input:
```
7
2 3
3 4
4 5
0 1
3 1
4 2
1 5
```
Output:
```
1.414214
```
