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.
def check(coor1, coor2, coor3):
    v1 = [coor2[i] - coor1[i] for i in range(5)]
    v2 = [coor3[i] - coor1[i] for i in range(5)]
    # print(v1, v2)
    return scalar_product(v1, v2)

def scalar_product(coor1, coor2):
    a1, a2, a3, a4, a5 = coor1
    b1, b2, b3, b4, b5 = coor2
    return (a1 * b1 + a2 * b2 + a3 * b3 + a4 * b4 + a5 * b5)
    
    
n = int(input())
idx___coor = []
for idx in range(n):
    coor = [int(x) for x in input().split()]
    idx___coor.append(coor)
if n > 129:
    print(0)
else:
    good_idxes = []
    for idx1, coor1 in enumerate(idx___coor):
        is_ok_flag = True
        for idx2, coor2 in enumerate(idx___coor):
            for idx3, coor3 in enumerate(idx___coor):
                # print(pairs_checked)
                if idx2 == idx3 or idx1 == idx3 or idx1 == idx2 or not is_ok_flag:
                    continue
                if check(coor1, coor2, coor3) > 0:
                    is_ok_flag = False
                # print(pairs_checked, is_ok_flag, idx1, idx2, idx3)
        if is_ok_flag:
            good_idxes.append(idx1)
                
    good_idxes = sorted(good_idxes)
    good_idxes = [(x + 1) for x in good_idxes]
    print(len(good_idxes))
    print(*good_idxes)
