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 sc(x, y):
    return x[0] * y[0] + x[1] * y[1] + x[2] * y[2] + x[3] * y[3] + x[4] * y[4]
def check(a, b, c):
    if sc([b[0] - a[0], b[1] - a[1], b[2] - a[2], b[3] - a[3], b[4] - a[4]], [c[0] - a[0], c[1] - a[1], c[2] - a[2], c[3] - a[3], c[4] - a[4]]) > 0:
        return True
    return False

n = int(input())
data = []
for i in range(n):
    a = list(map(int, input().split()))
    data.append(a)

an = 0
t = False
ann = []
for i in range(n):
    for j in range(n):
        if i == j:
            continue
        for k in range(n):
            if k == i or k == j:
                continue
            if check(data[i], data[j], data[k]):
                an += 1
                t = True
                break
        if t:
            break
    if not t:
        ann.append(i + 1)
    t = False

print(n - an)
print(*ann)
