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 sys
from math import acos, sqrt, pi
n = int(input())
p = []
def get_angle(a, b, c):
    v = [(b[i]-a[i], c[i]-a[i]) for i in range(5)]
    sp = sum([v[i][0]*v[i][1] for i in range(5)])
    sab = sqrt(sum([v[i][0]*v[i][0] for i in range(5)]))
    sac = sqrt(sum([v[i][1]*v[i][1] for i in range(5)]))
    if 2*acos(sp/(sab*sac))< pi:
        return True
    else:
        return False

for i in range(n):
    p.append(list(map(int, input().split())))
if n>38:
    print('0')
    sys.exit()
s = set()
t = [False]*n
for k in range(n):
    if not t[k]:
        for i in range(n):
            if k != i:
                for j in range(n):
                    if i != j and k != j:
                        if get_angle(p[k],p[i],p[j]):
                            s.add(k)
                            t[k] = True
                        if get_angle(p[i],p[k],p[j]):
                            s.add(i)
                            t[i] = True
                        if get_angle(p[j],p[k],p[i]):
                            s.add(j)
                            t[j] = True  
                    if t[k]:
                        break
                if t[k]:
                    break
        t[k] = True
s = sorted(list(set([i for i in range(n)]) - s))
print(len(s))
[print(i+1) for i in s]
                        
