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.
from math import acos, sqrt, degrees


class BadPoint(Exception):
    pass


def vect(point1, point2):
    return [p2 - p1 for p1, p2 in zip(point1, point2)]


def product(vect1, vect2):
    return sum([v1*v2 for v1, v2 in zip(vect1, vect2)])


def angle(vect1, vect2):
    return degrees(acos(product(vect1, vect2)/(sqrt(product(vect1, vect1))*sqrt(product(vect2, vect2)))))

n = int(input())
points = []
for _ in range(n):
    points.append(list(map(int, input().split())))

if n > 15:
    print(0)
    exit(0)
cnt = []
for i in range(n):
    vectors = []
    for j in range(n):
        if i != j:
            vectors.append(vect(points[i], points[j]))
    try:
        for ii in range(len(vectors)):
            for jj in range(len(vectors)):
                if ii != jj:
                    if angle(vectors[ii], vectors[jj]) < 90:
                        raise BadPoint()
    except BadPoint:
        pass
    else:
        cnt.append(i)

print(len(cnt))
print(*sorted(map(lambda x: x+1, cnt)), sep='\n')

