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.
#!/usr/bin/env python
from functools import reduce
from itertools import combinations

def inner_prod(v1, v2):
    assert len(v1) == len(v2)
    return reduce(lambda acc, pair: acc + pair[0] * pair[1], zip(v1, v2), 0)

def vec_diff(v1, v2):
    assert len(v1) == len(v2)
    return list(map(lambda pair: pair[0] - pair[1], zip(v1, v2)))

def is_good_triple(orig, v1, v2):
    return inner_prod(vec_diff(v1, orig), vec_diff(v2, orig)) <= 0

def process(vec_indx, vec_list, bad_set):
    for pair in combinations(range(len(vec_list)), 2):
        if vec_indx in pair:
            continue
        elif not is_good_triple(vec_list[vec_indx], vec_list[pair[0]], vec_list[pair[1]]):
            bad_set.add(vec_indx)
            return
        else:
            bad_set.add(pair[0])
            bad_set.add(pair[1])

def main():
    n = int(input())
    if n < 3:
        print(n)
        list(map(print, range(1, n+ 1)))
        return
    vec_list = [None] * n
    for indx in range(n):
        vec_list[indx] = list(map(int, input().split()))
    bad_set = set()
    for indx in range(n):
        if indx in bad_set:
            continue
        process(indx, vec_list, bad_set)

    print(n - len(bad_set))
    for indx in range(n):
        if indx not in bad_set:
            print(indx + 1)

main()
