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 math import *

n = int(input())
arr = [list(map(int, input().split())) for i in range(n)]
ans = [True] * n
for a in range(n):
    for b in range(n):
        bad = False
        for c in range(n):
            if arr[b] != arr[a] and arr[c] != arr[a] and arr[b] != arr[c]:
                ab = [arr[b][i] - arr[a][i] for i in range(5)]
                ac = [arr[c][i] - arr[a][i] for i in range(5)]
                sc = sum([ab[i] * ac[i] for i in range(5)])
                lab = (sum([ab[i] ** 2 for i in range(5)])) ** 0.5
                lac = (sum([ac[i] ** 2 for i in range(5)])) ** 0.5
                try:
                    if degrees(acos(sc / (lab * lac))) < 90:
                        ans[a] = False
                        bad = True
                        break
                except:
                    pass
        if bad:
            break
print(sum(ans))
for i in range(n):
    if ans[i]:
        print(i + 1)
