Closest Pair of Points

Problem Description

Given $n$ points on a plane, find the Euclidean distance between the closest pair of points.

Input Format

The first line contains an integer $n$.

The next $n$ lines each contain two numbers $x_i, y_i$, the coordinates of a point.

Output Format

Output one number, the answer. A relative or absolute error within $10^{-6}$ is accepted.

Sample Input

3
1.0 2.0
1.0 3.0
1.0 5.0

Sample Output

1.00000000

Constraints

For $100\%$ of the data: $1 \leq n \leq 2 \times 10^5$, $0 \leq x_i, y_i \leq 10^9$.