Given n points on the plane, each represented by (x, y) coordinates, find a pair of points with the smallest distance between them.

The first line of input will contain the number of points, n (2 <= n <= 30,000). Each of the next n lines will contain two integers x and y (-1,000,000 <= x, y <= 1,000,000). The ith line contains the coordinates for the ith point.

Output

Print to the ouput a single floating point number d, denoting the distance between the closest pair of points. d should contain exactly 6 digits after the decimal.

Example

Input:
5
0 0
-4 1
-7 -2
4 5
1 1


Output:
1.414214