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:

n = int(input())
l = []




def cross(x1,y1,x2,y2):

    area = x1*y2 - y1*x2
    return area


for i in range(n):
    x,y = map(int,input().split())
    l.append([x,y])
max_upper = 0
max_lower = 0
ans = 0
for i in range(n-1):
    for j in range(i+1,n):
        max_upper = 0
        max_lower = 0
        for k in range(n):
          if i!=j and i!=k and j!=k:
            area = (l[j][0] - l[i][0])*(l[k][1] - l[i][1])-(l[j][1] - l[i][1])*(l[k][0] - l[i][0])
            # print(area/2)
            if area>0:
                if area>max_upper:
                    max_upper = area
            else:
                if -area>max_lower and area!=0:
                    max_lower = -area

        if max_lower + max_upper > ans and max_lower!=0 and max_upper!=0:
          ans = max_lower + max_upper
print(ans/2)