Problem: Iahub has drawn a set of n points in the cartesian plane which he calls "special points". A quadrilateral is a simple polygon without self-intersections with four sides (also called edges) and four vertices (also called corners). Please note that a quadrilateral doesn't have to be convex. A special quadrilateral is one which has all four vertices in the set of special points. Given the set of special points, please calculate the maximal area of a special quadrilateral. 

Input

The first line contains integer n (4 ≤ n ≤ 300). Each of the next n lines contains two integers: xi, yi ( - 1000 ≤ xi, yi ≤ 1000) — the cartesian coordinates of ith special point. It is guaranteed that no three points are on the same line. It is guaranteed that no two points coincide. 

Output

Output a single real number — the maximal area of a special quadrilateral. The answer will be considered correct if its absolute or relative error does't exceed 10 - 9.

Examples

Input

5
0 0
0 4
4 0
4 4
2 3


Output

16.000000

Note

In the test example we can choose first 4 points to be the vertices of the quadrilateral. They form a square by side 4, so the area is 4·4 = 16.

Solution (in PYTHON3):

Solution:
import sys
c, n = 0, int(input())
t = list(map(int, sys.stdin.read().split()))
p = [complex(t[i], t[i + 1]) for i in range(0, 2 * n, 2)]
for x, i in enumerate(p, 1):
    for j in p[x:]:
        a = b = 0
        for k in p:
            if k == i or k == j: continue
            d = (i.real - k.real) * (j.imag - k.imag) - (i.imag - k.imag) * (j.real - k.real)
            a, b = min(d, a), max(d, b)
        if a and b: c = max(c, b - a)
print(c / 2)