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Time Limit: 1.0 s

Memory Limit: 256.0 MB

In a secluded ancient forest, a treasure map has led you to a set of \(N\) mystical relics scattered across a wide clearing. Each relic, located at specific coordinates \((x_i,y_i)\) on the map, contains clues to unlocking a grand hidden treasure. However, before you can collect them, you must safeguard these relics from a powerful curse that looms over the forest.

As the Treasure Keeper, you possess a magical artifact capable of creating a protective circle to shield the relics from the curse. However, the artifact’s magic is limited — the larger the circle, the faster its power depletes. To preserve energy, you must determine the smallest possible radius for this circle that will encompass all \(N\) relics.

Input

First line \(N\) The number of relics.
Each relic’s contains two integers value \(x_i\) and \(y_i\).

\(1 ≤ N ≤ 100\)
\(0 ≤ x_i , y_i ≤ 1000\)

Output

Print the minimum radius \(R\) of a circle that can enclose all \(N\) mystical relics, ensuring each relic is either inside or on the circle.

Your answer will be considered correct if the absolute or relative error does not exceed \(10^{-6}\).

Sample

3
0 0
0 1
1 0

0.707106781186497524

2
0 0
1 0

0.500000000000000000