Closest Pair

For given n points in metric space, find the distance of the closest points.

Constraints

• 2 ≤ n ≤ 100,000
• -100 ≤ x, y ≤ 100

Input

n x0 y0 x1 y1 : xn-1 yn-1

The first integer n is the number of points.

In the following n lines, the coordinate of the i-th point is given by two real numbers xi and yi. Each value is a real number with at most 6 digits after the decimal point.

Output

Print the distance in a line. The output values should be in a decimal fraction with an error less than 0.000001.

Examples

Input

2 0.0 0.0 1.0 0.0

Output

1.000000

Input

3 0.0 0.0 2.0 0.0 1.0 1.0

Output

1.41421356237

inputFormat

Input

n x0 y0 x1 y1 : xn-1 yn-1

The first integer n is the number of points.

In the following n lines, the coordinate of the i-th point is given by two real numbers xi and yi. Each value is a real number with at most 6 digits after the decimal point.

outputFormat

Output

Print the distance in a line. The output values should be in a decimal fraction with an error less than 0.000001.

Examples

Input

2 0.0 0.0 1.0 0.0

Output

1.000000

Input

3 0.0 0.0 2.0 0.0 1.0 1.0

Output

1.41421356237

样例

3
0.0 0.0
2.0 0.0
1.0 1.0

1.41421356237