You are given set of n points in 5-dimensional space. The points are labeled from 1 to n. No two points coincide.

We will call point a bad if there are different points b and c, not equal to a, from the given set such that angle between vectors <image> and <image> is acute (i.e. strictly less than <image>). Otherwise, the point is called good.

The angle between vectors <image> and <image> in 5-dimensional space is defined as <image>, where <image> is the scalar product and <image> is length of <image>.

Given the list of points, print the indices of the good points in ascending order.

Input

The first line of input contains a single integer n (1 ≤ n ≤ 103) — the number of points.

The next n lines of input contain five integers ai, bi, ci, di, ei (|ai|, |bi|, |ci|, |di|, |ei| ≤ 103) — the coordinates of the i-th point. All points are distinct.

Output

First, print a single integer k — the number of good points.

Then, print k integers, each on their own line — the indices of the good points in ascending order.

Examples

Input

6
0 0 0 0 0
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1


Output

1
1


Input

3
0 0 1 2 0
0 0 9 2 0
0 0 5 9 0


Output

0

Note

In the first sample, the first point forms exactly a <image> angle with all other pairs of points, so it is good.

In the second sample, along the cd plane, we can see the points look as follows:

<image>

We can see that all angles here are acute, so no points are good.
def inprod(a, b, c):
    v1 = [b[i] - a[i] for i in range(5)]
    v2 = [c[i] - a[i] for i in range(5)]
    return sum([v1[i] * v2[i] for i in range(5)])

n = int(raw_input())
points = []
for _ in range(n):
    a, b, c, d, e = map(int, raw_input().split(' '))
    points.append([a, b, c, d, e])
if n == 1:
    print 1
    print 1
elif n == 2:
    print 2
    print 1
    print 2
elif n > 50:
    print 0
else:
    for n1 in range(n):
        success = True
        for n2 in range(n):
            for n3 in range(n):
                if n1 == n2 or n2 == n3 or n1 == n3:
                    continue
                p1 = points[n1]
                p2 = points[n2]
                p3 = points[n3]
                if inprod(p1, p2, p3) > 0:
                    success = False
                    break
            if not success:
                break
        if success:
            print 1
            print n1 + 1
            break
    if not success:
        print 0
