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:
def diff(i):
    cp, np = points[i:i + 2]
    return np - cp


def cross(a, b):
    return a.real * b.imag - a.imag * b.real


def diameter(i, j):
    return abs(points[i] - points[j])


n = int(input())
t_points = [tuple(map(float, input().split())) for _ in range(n)]
i = min(range(n), key=lambda x: t_points[x])
j = max(range(n), key=lambda x: t_points[x])
points = [re + 1j * im for re, im in t_points]
points.append(points[0])
tentative_diameter = diameter(i, j)

it, jt = i, j
while True:
    if cross(diff(it), diff(jt)) >= 0:
        jt = (jt + 1) % n
    else:
        it = (it + 1) % n
    tentative_diameter = max(tentative_diameter, diameter(it, jt))

    if it == i and jt == j:
        break

print(tentative_diameter)