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.
def check(p1,p2,p3):
    s=0
    for i in range(5):
        s+=(p1[i]-p3[i])*(p2[i]-p3[i])
    if s>0:
        return True
    else:
        return False
def check1(p,pl):
    for i in range(1,len(pl)):
        for j in range(i+1,len(pl)):
            if check(pl[i],pl[j],p):
                return False
    return True
n=input()
pl=[[]]
for i in range(n):
    pl.append([int(j) for j in raw_input().split()])
if n==1:
    print 1
    print 1
elif n==2:
    print 2
    print 1
    print 2
else:
    i=1
    j=2
    k=3
    while(k<=n):
        if check(pl[j],pl[k],pl[i]):
            i,j=j,k
            k+=1
        else:
            j=k+1
            k=k+2
    if i<=n and check1(pl[i],pl[:i]+pl[i+1:]):
        print 1
        print i
    elif j<=n and check1(pl[j],pl[:j]+pl[j+1:]):
        print 1
        print j
    else:
        print 0
        
    
            
        
            
        
