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.
import math
n = int(raw_input())

pts = []
for _ in range(n):
    pts.append(map(float, raw_input().split()))

def get_dist2(p1, p2):
    return sum((p1[i] - p2[i])**2 for i in range(5))

D = [[0. for _ in range(n) ] for _ in range(n)]

for i in range(n):
    for j in range(i):
        tmp = get_dist2(pts[i], pts[j])
        D[i][j] = tmp
        D[j][i] = tmp

def check(i):
    for j in range(n):
        if j == i:
            continue
        AC = D[i][j]
        for k in range(j):
            if k == i:
                continue
            BC = D[i][k]
            AB = D[j][k]
            if AC + BC - AB > 0:
                return False
    return True

cnt = 0
ans = []
for i in range(n):
    is_good = check(i)
    if is_good:
        cnt += 1
        ans.append(str(i + 1))
print cnt
if cnt > 0:
    print ' '.join(ans)
