Sadly, this is the last time Sean will play James Bond.

His mission is to network $n$ antennas that are scattered across a vast desert, which can be represented as a 2D plane. He will set the transmission radius of each antenna to be the same non-negative real number $r$. The range of an antenna is defined as the set of all points whose distance to the antenna is at most $r$. If ranges of two antennas have a common point, those antennas can directly communicate. Also, if antennas $A$ and $B$ can communicate, as well as antennas $B$ and $C$, then antennas $A$ and $C$ are also able to communicate, through antenna $B$.

Sean wants to network the antennas, i.e. make it possible for every two antennas to communicate. Since M has limited his spending for this mission, and larger radii require more money, Sean will choose the smallest possible radius $r$. Help him solve this problem!

Input

The first line contains an integer $n$ $(1\le n\le 1000)$, the number of antennas.

Each of the following $n$ lines contains integers $x_i$ and $y_i$ $(0\le x_i,y_i\le {10}^9)$, coordinates of the $i$-th antenna.

Output

Output the minimal radius.

Your answer will be considered correct if its absolute or relative error doesn't exceed ${10}^{-6}$.

Scoring

In test cases worth $50\mathrm{\%}$ points it holds that $1\le n\le 100$.

Sample Input 1

2
1 1
2 2

Sample Output 1

0.7071068

Sample Input 2

7
2 3
3 4
4 5
0 1
3 1
4 2
1 5

Sample Output 2

1.4142135

Explanation for Sample Output 2

Sample Input 3

4
2020 20
20 2020
2020 2020
20 20

Sample Output 3

1000.0000000