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;
  scanf("%d", &n);
  int arr[n][5];
  int ta, tb, tc, td, te;
  for (int i = 0; i < n; i++) {
    scanf("%d %d %d %d %d", &ta, &tb, &tc, &td, &te);
    arr[i][0] = ta;
    arr[i][1] = tb;
    arr[i][2] = tc;
    arr[i][3] = td;
    arr[i][4] = te;
  }
  set<int> ans;
  for (int i = 0; i < n; i++) {
    bool good = true;
    for (int j = 0; j < n && good; j++) {
      if (i == j) {
        continue;
      }
      for (int k = 0; k < n && good; k++) {
        if (k == i || k == j) {
          continue;
        }
        int ab[5] = {arr[j][0] - arr[i][0], arr[j][1] - arr[i][1],
                     arr[j][2] - arr[i][2], arr[j][3] - arr[i][3],
                     arr[j][4] - arr[i][4]};
        int ac[5] = {arr[k][0] - arr[i][0], arr[k][1] - arr[i][1],
                     arr[k][2] - arr[i][2], arr[k][3] - arr[i][3],
                     arr[k][4] - arr[i][4]};
        int abdotac = 0;
        for (int i = 0; i < 5; i++) {
          abdotac += ab[i] * ac[i];
        }
        int barab = 0;
        int barac = 0;
        for (int i = 0; i < 5; i++) {
          barab += ab[i] * ab[i];
          barac += ac[i] * ac[i];
        }
        double angle = (double)abdotac / ((double)barab * (double)barac);
        if (angle > 0.0) {
          good = false;
          break;
        }
      }
    }
    if (good) {
      ans.insert(i);
    }
  }
  int si = ans.size();
  printf("%d\n", si);
  for (auto a : ans) {
    printf("%d\n", a + 1);
  }
  return 0;
}
