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:
def cross(x1, y1, x2, y2):
    return x1 * y2 - x2 * y1

def gao():
    n = int(input())
    x, y = [], []
    for i in range(n):
        x1, y1 = input().split(' ')
        x.append(int(x1))
        y.append(int(y1))

    max_area = 0
    for i in range(n):
        for j in range(i+1, n):
            max_left, max_right = 0, 0
            for k in range(n):
                if i != k and j != k:
                    area = cross(x[j] - x[i], y[j] - y[i], x[k] - x[i], y[k] - y[i])
                    if area > 0:
                        max_left = max(max_left, area)
                    elif area < 0:
                        max_right = max(max_right, -area)
            if max_left != 0 and max_right != 0:
                max_area = max(max_area, max_left + max_right)

    print(max_area / 2.)

gao()