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 *
n=input()
a=[map(int,raw_input().split()) for i in range(n)]
if n>15:
    print 0
    exit(0)
def dot(a,b):
    return sum([i*j for i,j in zip(a,b)])
def diff(a,b):
    return [i-j for i,j in zip(a,b)]
def mod(a):
    return sum([i*i for i in a])**0.5
ans=[]
for i in range(n):
    curr=True
    for j in range(n):
        if i == j:continue
        for k in range(n):
            if k in[i,j]:continue
            if abs(acos(dot(diff(a[j],a[i]), diff(a[k],a[i])) / (mod(diff(a[j],a[i]))*mod(diff(a[k],a[i]))))) < pi/2:
                curr=False
    if curr:ans.append(i+1)
print len(ans)
print " ".join(map(str, ans))
