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 collections import Counter
import math

def dotproduct(v1, v2):
    return sum((a*b) for a, b in zip(v1, v2))

def length(v):
    return math.sqrt(dotproduct(v, v))

def angle(v1, v2):
    temp = dotproduct(v1, v2) / (length(v1) * length(v2))
    if temp<-1: temp = -1.0
    if temp>1: temp = 1.0
    return math.acos(temp)

def vec(a,b):
    return b[0]-a[0],b[1]-a[1],b[2]-a[2],b[3]-a[3],b[4]-a[4]

n = input()
pts = []
for i in range(n):
    pts.append(map(float,raw_input().strip().split()))
ans = []
for i in xrange(n):
    done = False
    for j in xrange(n):
        for k in xrange(j+1,n):
            if i!=j and i!=k and j!=k:
                if angle(vec(pts[i],pts[j]),vec(pts[i],pts[k]))<(math.pi/2.0):
                    done = True
                    break
        if done:
            break
    if not done:
        ans.append(i+1)
print len(ans)
if ans:
    print "\n".join(map(str,ans))