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;
  cin >> n;
  int a[n], b[n], c[n], d[n], e[n];
  for (int i = 0; i < n; i++) {
    cin >> a[i] >> b[i] >> c[i] >> d[i] >> e[i];
  }
  int ar[n];
  memset(ar, 1, sizeof ar);
  int j = 0, k, l;
  int i = 0;
  while (1) {
    j, k, l;
    k = i + 1;
    l = i + 2;
    if (l > n - 1) break;
    int d1 = ((a[j] - a[k]) * (a[j] - a[k]) + (b[j] - b[k]) * (b[j] - b[k]) +
              (c[j] - c[k]) * (c[j] - c[k]) + (d[j] - d[k]) * (d[j] - d[k]) +
              (e[j] - e[k]) * (e[j] - e[k]));
    int d2 = ((a[j] - a[l]) * (a[j] - a[l]) + (b[j] - b[l]) * (b[j] - b[l]) +
              (c[j] - c[l]) * (c[j] - c[l]) + (d[j] - d[l]) * (d[j] - d[l]) +
              (e[j] - e[l]) * (e[j] - e[l]));
    int d3 = ((a[l] - a[k]) * (a[l] - a[k]) + (b[l] - b[k]) * (b[l] - b[k]) +
              (c[l] - c[k]) * (c[l] - c[k]) + (d[l] - d[k]) * (d[l] - d[k]) +
              (e[l] - e[k]) * (e[l] - e[k]));
    if (d1 + d2 + d3 - max(d3, max(d1, d2)) > max(d3, max(d1, d2))) {
      ar[j] = 0;
      ar[k] = 0;
      ar[l] = 0;
      i += 3;
      j = i;
    } else {
      i += 2;
      if (d1 == max(d1, max(d2, d3))) {
        ar[j] = 0;
        ar[k] = 0;
        j = l;
      } else if (d2 == max(d1, max(d2, d3))) {
        ar[j] = 0;
        ar[l] = 0;
        j = k;
      } else if (d3 == max(d1, max(d2, d3))) {
        ar[l] = 0;
        ar[k] = 0;
      }
    }
  }
  for (int x = 0; x < n; x++) {
    int flag = 0;
    if (ar[x] == 0) continue;
    for (int y = 0; y < n; y++) {
      if (x == y) {
        continue;
      }
      for (int z = 0; z < n; z++) {
        if (z == y || z == x) continue;
        j = x;
        k = y;
        l = z;
        int d1 =
            ((a[j] - a[k]) * (a[j] - a[k]) + (b[j] - b[k]) * (b[j] - b[k]) +
             (c[j] - c[k]) * (c[j] - c[k]) + (d[j] - d[k]) * (d[j] - d[k]) +
             (e[j] - e[k]) * (e[j] - e[k]));
        int d2 =
            ((a[j] - a[l]) * (a[j] - a[l]) + (b[j] - b[l]) * (b[j] - b[l]) +
             (c[j] - c[l]) * (c[j] - c[l]) + (d[j] - d[l]) * (d[j] - d[l]) +
             (e[j] - e[l]) * (e[j] - e[l]));
        int d3 =
            ((a[l] - a[k]) * (a[l] - a[k]) + (b[l] - b[k]) * (b[l] - b[k]) +
             (c[l] - c[k]) * (c[l] - c[k]) + (d[l] - d[k]) * (d[l] - d[k]) +
             (e[l] - e[k]) * (e[l] - e[k]));
        if (d1 + d2 + d3 - max(d3, max(d1, d2)) > max(d3, max(d1, d2))) {
          ar[j] = 0;
          flag = 1;
          break;
        } else {
          if (d1 == max(d1, max(d2, d3))) {
            ar[j] = 0;
            ar[k] = 0;
            flag = 1;
            break;
          } else if (d2 == max(d1, max(d2, d3))) {
            ar[j] = 0;
            ar[l] = 0;
            flag = 1;
            break;
          } else if (d3 == max(d1, max(d2, d3))) {
            ar[l] = 0;
            ar[k] = 0;
          }
        }
      }
      if (flag == 1) break;
    }
  }
  int cnt = 0;
  for (int i = 0; i < n; i++) {
    if (ar[i]) cnt++;
  }
  cout << cnt << endl;
  for (int i = 0; i < n; i++) {
    if (ar[i]) cout << i + 1 << endl;
  }
  return 0;
}
