Minimum Pair Distance

Given n points in the 2D plane, find the pair of points with the minimum Euclidean distance. In other words, among all \( {n \choose 2} \) pairs of points, determine the pair whose distance is the smallest.

The Euclidean distance between two points \( (x_i, y_i) \) and \( (x_j, y_j) \) is given by:

$$ d = \sqrt{(x_i - x_j)^2 + (y_i - y_j)^2} $$

inputFormat

The first line contains an integer n (n ≥ 2) denoting the number of points.

The following n lines each contain two real numbers x and y indicating the coordinates of each point.

outputFormat

Output a single line with the minimum Euclidean distance among all pairs of points. The answer should be printed with 6 decimal places of precision.

sample

2
0 0
0 1

1.000000