Given several points on the plane, compute the Euclidean distance between the closest pair.

Input

Input consists of the coordinates of n different points.
The coordinates are real numbers with absolute value at most 10^{5}.
Assume 2 ≤ n ≤ 10^{5}.

Output

Print the smallest distance between all pairs of points, with five digits after the decimal point. The input cases have no precision issues.

Public test cases

**Input**

1.2 4.5 2.4 1.2 3.3 1.1 4.4 4.4 7.7 1.1 1.1 2.1 8.6 1.9 3.3 9.0

**Output**

0.90554

**Input**

1 1 2 2 3 3 4 4 5 5

**Output**

1.41421

Information

- Author
- Jordi Petit
- Language
- English
- Official solutions
- C++ Python
- User solutions
- C++ Python