Closest pair P70827

Statement

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 $2 \le n \le 10^5$ .

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

Output

1.41421

Information

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