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.
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, i, j, k, a, b, c, cnt;
  cin >> n;
  int co[n][5], ans[n];
  memset(ans, 0, sizeof ans);
  for (i = 0; i < n; i++)
    cin >> co[i][0] >> co[i][1] >> co[i][2] >> co[i][3] >> co[i][4];
  cnt = 0;
  for (i = 0; i < n - 2; i++)
    for (j = i + 1; j < n - 1; j++)
      for (k = j + 1; k < n; k++) {
        a = (co[i][0] - co[j][0]) * (co[j][0] - co[k][0]) +
            (co[i][1] - co[j][1]) * (co[j][1] - co[k][1]) +
            (co[i][2] - co[j][2]) * (co[j][2] - co[k][2]) +
            (co[i][3] - co[j][3]) * (co[j][3] - co[k][3]) +
            (co[i][4] - co[j][4]) * (co[j][4] - co[k][4]);
        b = (co[i][0] - co[k][0]) * (co[j][0] - co[k][0]) +
            (co[i][1] - co[k][1]) * (co[j][1] - co[k][1]) +
            (co[i][2] - co[k][2]) * (co[j][2] - co[k][2]) +
            (co[i][3] - co[k][3]) * (co[j][3] - co[k][3]) +
            (co[i][4] - co[k][4]) * (co[j][4] - co[k][4]);
        c = (co[i][0] - co[j][0]) * (co[i][0] - co[k][0]) +
            (co[i][1] - co[j][1]) * (co[i][1] - co[k][1]) +
            (co[i][2] - co[j][2]) * (co[i][2] - co[k][2]) +
            (co[i][3] - co[j][3]) * (co[i][3] - co[k][3]) +
            (co[i][4] - co[j][4]) * (co[i][4] - co[k][4]);
        if (c > 0) ans[i] = -1;
        if (b > 0) ans[k] = -1;
        if (-a > 0) ans[j] = -1;
      }
  for (i = 0; i < n; i++)
    if (ans[i] != -1) cnt++;
  cout << cnt << endl;
  for (i = 0; i < n; i++)
    if (ans[i] != -1) cout << i + 1 << ' ';
  return 0;
}
