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 math


def check(i, j, k):
    a = []
    b = []
    for ii in range(len(i)):
        a.append(j[ii] - i[ii])
        b.append(k[ii] - i[ii])
    la = 0
    lb = 0
    scal = 0
    for ii in range(len(i)):
        la += a[ii] * a[ii]
        lb += b[ii] * b[ii]
        scal += a[ii] * b[ii]
    return (scal / (la * lb)) <= 0


def count(w):
    ans = []
    for i in range(len(w)):
        f = 1
        for j in w:
            if (w[i] == j):
                continue
            for k in w:
                if (w[i] == k or j == k):
                    continue
                f &= check(w[i], j, k)
        ans += [i + 1] if f else []
    return [len(ans)] + ans



n = int(input())
w = []
for i in range(n):
    w.append(list(map(int, input().split())))
if (n < 20):
    print(*count(w), end='\n')
else:
    print(0)