Problem: 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

Solution (in PYTHON3):

Solution:
# Cross product
def cross(p1, p2, q1, q2):
    p = p2 - p1
    q = q2 - q1
    return p.real * q.imag - p.imag * q.real

# Rotating calipers
er = 1e-16

def convex_diameter(points, n):
    points.append(points[0])
    p0 = points[0]
    p1 = points[1]
    for i, (q1, q2) in enumerate(zip(points[1:], points[2:]), start=1):
        if cross(p0, p1, q1, q2) < -er:
            break
    
    max_d = abs(points[i] - points[0])

    points.append(points[1])
    side1 = zip(points[0:i+1], points[1:i+2])
    side2 = zip(points[i:n+1], points[i+1:])
    p1, p2 = side1.__next__()
    q1, q2 = side2.__next__()
    
    for i in range(n - 1):
        if cross(p1, p2, q1, q2) > er:
            q1, q2 = side2.__next__()
        else:
            p1, p2 = side1.__next__()
        max_d = max(max_d, abs(p1 - q1))

    return max_d

# Acceptance of input
def string_to_complex(s):
    x, y = map(float, s.split())
    return x + y * 1j

import sys

file_input = sys.stdin

n = int(file_input.readline())

P = [string_to_complex(line) for line in file_input]

# Output
ans = convex_diameter(P, n)
print('{:f}'.format(ans))