On the opening ceremony of World Cup there was a part where many kids from around the world was trying to make a big circle on the field which symbolized tolerance and multicultural friendship.

They succeed in making a perfect circle, but as they didn't practice very much, kids weren't uniformly distributed on circle. You spotted that very quickly, and you want to know what is the minimum distance between some two kids.

Input

First line of the input contains number N (2 <= N <= 10⁵) representing number of kids. Each of next N lines contains two real numbers rounded on two decimal places – coordinates of the each kid. It is guaranteed that all points will be on circle.

All coordinates will be in interval [-10⁶, 10⁶]. In 20% of test cases it will hold N <= 10³

Output

First and only line of output should contain one real number (rounded on two decimal places) – Euclidian distance between two nearest kids. Euclidian distance between points (x1, y1) and (x2, y2) is the square root of: (x2-x1)² + (y2-y1)².

Constraints

Time limit: 1500 milliseconds
Memory limit: 64 megabytes

Examples

input
5
1.00 4.00
-0.50 -1.60
4.00 1.00
3.12 3.12
-1.60 -0.50

output
1.56

Kids at points (-0.50, -1.60) and (-1.60, -0.50) are nearest and distance between them is 1.56.