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
#sys.stdin = open('input.txt', 'r')
#sys.stdout = open('output.txt','w')
def angle(a,b,c) :
    res = 0
    for i in xrange(len(b)) :
        x = b[i] - a[i]
        y = c[i] - a[i]
        res += x*y
    return res

raw_input = sys.stdin.readline
N = int(raw_input().strip())
A = []
ans = []
for _ in xrange(N) :
    A += map(int, raw_input().strip().split(' ')),
for i in xrange(N) :
    flag = False
    for j in xrange(N) :
        for k in xrange(N) :
            if j != i and k != i and k != j and angle(A[i],A[j],A[k]) > 0 :
                flag = True
                break
        if flag == True :
            break
    if flag == False :
        ans += i,
print len(ans)
for x in ans :
    print x+1