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

good_dots = []

for a_index in range(n):
	a_dot = dots[a_index]
	a_is_good = True
	for b_index in range(n):
		for c_index in range(n):
			if a_index != b_index and a_index != c_index and b_index < c_index:
				b_dot = dots[b_index]
				c_dot = dots[c_index]
				ab_vec = [b_coord - a_coord for a_coord, b_coord in zip(a_dot, b_dot)]
				ac_vec = [c_coord - a_coord for a_coord, c_coord in zip(a_dot, c_dot)]
				# print(ab_vec)
				# print(ac_vec)
				prod = sum([a * b for a, b in zip(ab_vec, ac_vec)])
				# print(prod)
				if prod > 0:
					a_is_good = False
					break
		if not a_is_good:
			break
	if a_is_good:
		good_dots.append(a_index + 1)

print(len(good_dots))
for dot in good_dots:
	print(dot)





