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.
# -*- coding: utf-8 -*-

import math
import collections
import bisect
import heapq
import time
import random
import itertools

"""
created by shhuan at 2017/10/19 17:35

"""
N = int(input())
P = []
for i in range(N):
    P.append([int(x) for x in input().split()])


def length(a):
    return math.sqrt(sum([x**2 for x in a]))

def angle(a, b):
    c = sum(a[i]*b[i] for i in range(len(a)))
    la = length(a)
    lb = length(b)
    if la and lb:
        return math.acos(c/la/lb)
    return -1

def cos(a, b, c):

    x = [b[i]-a[i] for i in range(len(a))]
    y = [c[i]-a[i] for i in range(len(a))]

    c = sum(x[i] * y[i] for i in range(len(x)))

    return c

ans = []
for i in range(N):
    bad = False
    for j in range(N):
        if bad:
            break
        if i != j:
            for k in range(N):
                if k != i and k != j:
                    if cos(P[i], P[j], P[k]) > 0:
                        bad = True
                        break
    if not bad:
        ans.append(i+1)
print(len(ans))
if ans:
    print(' '.join(map(str, ans)))