Diameter of a Convex Polygon

Find the diameter of a convex polygon g. In other words, find a pair of points that have maximum distance between them.

Constraints

• 3 ≤ n ≤ 80000
• -100 ≤ xi, yi ≤ 100
• No point in the g will occur more than once.

Input

n x1 y1 x2 y2 : xn yn

The first integer n is the number of points in g.

In the following lines, the coordinate of the i-th point pi is given by two real numbers xi and yi. The coordinates of points are given in the order of counter-clockwise visit of them. Each value is a real number with at most 6 digits after the decimal point.

Output

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

Examples

Input

3 0.0 0.0 4.0 0.0 2.0 2.0

Output

4.00

Input

4 0.0 0.0 1.0 0.0 1.0 1.0 0.0 1.0

Output

1.414213562373

inputFormat

Input

n x1 y1 x2 y2 : xn yn

The first integer n is the number of points in g.

In the following lines, the coordinate of the i-th point pi is given by two real numbers xi and yi. The coordinates of points are given in the order of counter-clockwise visit of them. Each value is a real number with at most 6 digits after the decimal point.

outputFormat

Output

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

Examples

Input

3 0.0 0.0 4.0 0.0 2.0 2.0

Output

4.00

Input

4 0.0 0.0 1.0 0.0 1.0 1.0 0.0 1.0

Output

1.414213562373

样例

4
0.0 0.0
1.0 0.0
1.0 1.0
0.0 1.0

1.414213562373