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 inner(a, b):
  ret = 0
  for x, y in zip(a, b):
    ret += x * y
  return ret

def diff(a, b):
  ret = [0] * 5
  for i, (x, y) in enumerate(zip(a, b)):
    ret[i] = x - y
  return ret

def GoodPoints(n, PointsTab):
	if n>11:			#if there are more than 11 points there is no good point
		return [0,[]]
	else:
		GoodP = []
		for i in range(n):
			good = 1
			for j in range(n):
				for k in range(n):
					if j!=i and j!=k and k!=i:
						if inner(diff(PointsTab[j],PointsTab[i]),diff(PointsTab[k],PointsTab[i]))>0:
							good = 0
							break
				if good == 0:
					break
			if good == 1:
				GoodP.append(i+1)
	return [len(GoodP),GoodP]


n = map(int, raw_input().split(' '))[0]
PointsTab = []
for i in range(n):
	PointsTab.append(map(int, raw_input().split(' ')))

GoodP = GoodPoints(n, PointsTab)
print GoodP[0]
for i in range(GoodP[0]):
	print GoodP[1][i]
