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

ans=[]

for i in range(n):
    Flag=True
    for j in range(n):
        if j!=i and Flag==True:
            for k in range(j+1,n):
                if i!=k:
                    s=0
                    for x in range(5):
                        s+=(A[j][x]-A[i][x])*(A[k][x]-A[i][x])
                    if s>0:
                        Flag=False
                        break
    if Flag==True:
        ans.append(i)

print len(ans)
if len(ans)>0:
    for i in range(len(ans)):
        print ans[i]+1

